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## "Análise bayesiana da probabilidade de permanência no rebanho como característica de seleção para a raça Nelore" ; Bayesian inference for stayability as selection criteria in Nelore beef cattle

Fonte: Biblioteca Digitais de Teses e Dissertações da USP
Publicador: Biblioteca Digitais de Teses e Dissertações da USP

Tipo: Tese de Doutorado
Formato: application/pdf

Publicado em 12/09/2003
PT

Relevância na Pesquisa

46.22%

#Bayesian methodology#Bovine#Bovino#Componentes de (co)variância#Components of (co)variance#Correlações entre classificações#Diferença Esperada na Progênie#Expected Progeny Differences#Genetic Parameters#metodologia Bayesiana#Nelore

As novas biotecnologias em reprodução, como a transferência de embriões e a fecundação in vitro, de certo modo, despertaram nos produtores e pesquisadores da área de melhoramento animal o interesse na seleção de fêmeas, antes pouco explorada dada a grande ênfase empregada na seleção e avaliação de reprodutores machos. A cada ano é percebido que a pecuária de corte funciona como uma empresa e, como tal, deve-se preocupar com todos os detalhes e não enfocando apenas um, como o mais importante, e é com isso que o Programa de Melhoramento Genético da Raça Nelore (PMGRN-USP) estuda cada vez mais um número maior de características como, stayability e suas possíveis aplicações à seleção das vacas Nelore, pois tem grande importância econômica. Com o objetivo de analisar a característica stayability sob enfoque Bayesiano, em registros de produção de vacas da raça Nelore, inicialmente foram implementados dois tamanhos de cadeia de Gibbs (225 ou 550 mil), dois períodos de descarte amostral (25 ou 50 mil) e duas formas de tomadas de amostra (a cada 1000 ou 250 rodadas). Os registros foram codificados como 0 (fracasso, ou menos de três partos até os 6 anos de idade) ou 1 (sucesso, ou pelo menos três partos até os 6 anos de idade) e os arquivos sofreram restrição ou não para NEP (Número Efetivo de Progênie)...

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## Genetic avaluacion for persistency of lactation in Holstein cows using a random regression model

Fonte: Universidade Federal do Rio Grande do Sul
Publicador: Universidade Federal do Rio Grande do Sul

Tipo: Artigo de Revista Científica
Formato: application/pdf

ENG

Relevância na Pesquisa

45.97%

#Genetica animal#Genetic evaluation#Persistency of lactation#Lactação#Produção animal#Rank correlation#Random regression models

A model for analyzing test day records including both fixed and random coefficients was applied to the genetic evaluation of first lactation data for Holstein cows. Data comprising 87045 test-day milk yield records from calving between 1997 and 2001 from Holstein herds in 10 regions of the Brazilian state of Minas Gerais. Six persistency of lactation measures were evaluated using breeding values obtained by random regression analyses. The Wilmink function was used to model the additive genetic and permanent environmental effects. Residual variance was constant throughout lactation. Ranking for animals did not change among criteria for persistency measurements, but ranking changes were observed when the estimated breeding value (EBV) for persistency of lactation was contrasted with those estimated for 305-day milk yield (305MY). The rank correlation estimates for persistency of lactation and 305MY were practically the same for sire and cows, and ranged from -0.45 to 0.69. The EBVs for milk yield during lactation for sires producing daughters with superior 305MY indicate genetic differences between sires regarding their ability to transmit desirable persistency of lactation traits. This suggests that selection for total lactation milk yield does not identify sires or cows that are genetically superior in regard to persistency of lactation. Genetic evaluation for persistency of lactation is important for improving the efficiency of the milk production capacity of Holstein cows.

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## Avaliação genética de touros da raça Gir para produção de leite no dia do controle e em 305 dias de lactação

Fonte: Sociedade Brasileira de Zootecnia
Publicador: Sociedade Brasileira de Zootecnia

Tipo: Artigo de Revista Científica
Formato: 1964-1972

POR

Relevância na Pesquisa

45.97%

#animal breeding#Dairy cattle#milking control#Rank correlation#Bovino de leite#controle leiteiro#melhoramento animal

Dados de 32.779 controles mensais, de 3.605 lactações em 305 dias (PL305), de 2.082 vacas Gir, filhas de 281 touros, com partos ocorridos de 1987 a 1999 em 11 rebanhos, foram usados com o objetivo de verificar a viabilidade de utilização da produção de leite no dia do controle (PLDC) em avaliações genéticas de touros da raça Gir. Foram realizadas análises univariadas das PLDC1 a PLDC10 e da PL305 pelo método de máxima verossimilhança restrita, sob modelo animal, incluindo as três primeiras lactações como medidas repetidas de um mesmo animal, diferenciados conforme o grupo contemporâneo de rebanho-ano-estação, de acordo com a idade da vaca ao parto e, do intervalo parto-primeiro controle na PLDC1. As médias observadas e os respectivos desvios-padrão (kg) para PLDC1 a PLDC10 e PL305 foram: 11,97±4,64; 11,93±4,68; 10,98±4,40; 10,18±4,12; 9,66±3,88; 9,20±3,69; 8,63±3,51; 8,08±3,33; 7,59±3,27; 7,22±3,15 e 2.746,17±1.299,90. As estimativas de herdabilidade para as PLDC1 a PLDC10 foram de 0,26; 0,19; 0,18; 0,20; 0,15; 0,13; 0,14; 0,10; 0,11 e 0,10, respectivamente; para a PL305 foi de 0,18. As correlações de ordem dos valores genéticos preditos de 281 touros, obtidos entre as PLDC e a PL305, foram altas...

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## Comparação entre critérios de seleção de precocidade sexual e a associação destes com características de crescimento em bovinos Nelore

Fonte: Sociedade Brasileira de Zootecnia
Publicador: Sociedade Brasileira de Zootecnia

Tipo: Artigo de Revista Científica
Formato: 93-100

POR

Relevância na Pesquisa

36.2%

#average daily gain#days to gain 160 kg from birth to weaning#Genetic correlation#Heritability#Rank correlation#scrotal circumference corrected to age and live weight#Correlação genética#correlação de rank#dias para ganhar 160 kg#Ganho médio diário#Herdabilidade

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES); Neste trabalho estimaram-se parâmetros genéticos do perímetro escrotal (PE), PE corrigido para idade (PEi) e PEi corrigido para peso corporal (PEip) de bovinos Nelore, comparando-se a classificação dos animais pelas DEPs, segundo o critério adotado. Além disso, estimaram-se a correlação genética existente entre as três expressões do PE e o ganho médio diário pré-desmama, o ganho médio diário pós-desmama, o número de dias para ganhar 160 kg após o nascimento e o número de dias para ganhar 240 kg após a desmama. As informações foram obtidas nos Registros de Produção da Associação Paraguaia dos Criadores de Nelore, entre 1986 e 1997, em 110 rebanhos. As estimativas dos componentes de variância e herdabilidade foram obtidas pelo Método da Máxima Verossimilhança Restrita, usando modelos animais uni característica. As herdabilidades estimadas foram 0,41; 0,40; e 0,47 para PE, PEi e PEip, respectivamente, todas indicando possibilidade de progresso genético por seleção. A estimativa de correlação genética entre PEi e PEip (0,62) foi moderada e os valores obtidos para as correlações entre as características de precocidade sexual e de crescimento foram de pequena magnitude. As estimativas de correlações de rank das DEPs foram 0...

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## Age-age correlation for early selection of rubber tree genotypes in São Paulo State, Brazil

Fonte: Universidade Estadual Paulista
Publicador: Universidade Estadual Paulista

Tipo: Artigo de Revista Científica
Formato: 758-764

ENG

Relevância na Pesquisa

56.12%

#Early clonal multiplication#Evaluation of clones#Genetic correlation#Hevea brasiliensis#Rank correlation#latex#rubber#Brazil#clone#controlled study#genetic correlation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); In a field trial involving 68 rubber tree (Hevea spp.) clones calculation of genotypic correlation coefficients revealed significant age-age correlation from age 1 to 6 (immature period) for girth A and for age 7 to 12 (mature period) for girth B and for age 7 to 12 (production of latex) for yield. Rank correlation coefficients between all immature ages of girth (girth A), all ages of mature girth (girth B) and all annual rubber production (yield) were significant for the three traits, with the coefficients decreasing with increasing age. Selection of the sets of best 30, 15, 10 and 5 clones from the available 68 clones at a given age was generally accompanied by a descending order of percentage success. It was suggested: (a) to have the best 30 clones of age 6, select the set of best 36 clones at age 2, (b) to have the best 15 clones of age 6, select the set of best 20 clones at age 3, (c) to have the best 5 clones of age 6, select the set of best 8 clones at age 4, and (d) to have the best 3 clones of age 6, select the set of best 3 clones at age 5. More than 80% of the targeted clones on girth A or girth B basis and more than 76.7% clones on yield basis were found to get selected at steps (a) through (d). For achieving early multiplication of the most productive clone for deployment...

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## Age-age correlation for early selection of rubber tree genotypes in São Paulo State, Brazil

Fonte: Sociedade Brasileira de Genética
Publicador: Sociedade Brasileira de Genética

Tipo: Artigo de Revista Científica
Formato: text/html

Publicado em 01/12/2005
EN

Relevância na Pesquisa

56.1%

#Hevea brasiliensis#early clonal multiplication#genetic correlation#rank correlation#evaluation of clones

In a field trial involving 68 rubber tree (Hevea spp.) clones calculation of genotypic correlation coefficients revealed significant age-age correlation from age 1 to 6 (immature period) for girth A and for age 7 to 12 (mature period) for girth B and for age 7 to 12 (production of latex) for yield. Rank correlation coefficients between all immature ages of girth (girth A), all ages of mature girth (girth B) and all annual rubber production (yield) were significant for the three traits, with the coefficients decreasing with increasing age. Selection of the sets of best 30, 15, 10 and 5 clones from the available 68 clones at a given age was generally accompanied by a descending order of percentage success. It was suggested: (a) to have the best 30 clones of age 6, select the set of best 36 clones at age 2, (b) to have the best 15 clones of age 6, select the set of best 20 clones at age 3, (c) to have the best 5 clones of age 6, select the set of best 8 clones at age 4, and (d) to have the best 3 clones of age 6, select the set of best 3 clones at age 5. More than 80% of the targeted clones on girth A or girth B basis and more than 76.7% clones on yield basis were found to get selected at steps (a) through (d). For achieving early multiplication of the most productive clone for deployment...

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## Genetic evaluation for persistency of lactation in Holstein cows using a random regression model

Fonte: Sociedade Brasileira de Genética
Publicador: Sociedade Brasileira de Genética

Tipo: Artigo de Revista Científica
Formato: text/html

Publicado em 01/03/2007
EN

Relevância na Pesquisa

45.97%

A model for analyzing test day records including both fixed and random coefficients was applied to the genetic evaluation of first lactation data for Holstein cows. Data comprising 87045 test-day milk yield records from calving between 1997 and 2001 from Holstein herds in 10 regions of the Brazilian state of Minas Gerais. Six persistency of lactation measures were evaluated using breeding values obtained by random regression analyses. The Wilmink function was used to model the additive genetic and permanent environmental effects. Residual variance was constant throughout lactation. Ranking for animals did not change among criteria for persistency measurements, but ranking changes were observed when the estimated breeding value (EBV) for persistency of lactation was contrasted with those estimated for 305-day milk yield (305MY). The rank correlation estimates for persistency of lactation and 305MY were practically the same for sire and cows, and ranged from -0.45 to 0.69. The EBVs for milk yield during lactation for sires producing daughters with superior 305MY indicate genetic differences between sires regarding their ability to transmit desirable persistency of lactation traits. This suggests that selection for total lactation milk yield does not identify sires or cows that are genetically superior in regard to persistency of lactation. Genetic evaluation for persistency of lactation is important for improving the efficiency of the milk production capacity of Holstein cows.

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## Stochastic rank correlation: A robust merit function for 2D/3D registration of image data obtained at different energies

Fonte: PubMed
Publicador: PubMed

Tipo: Artigo de Revista Científica

Publicado em /08/2009
EN

Relevância na Pesquisa

46.15%

In this article, the authors evaluate a merit function for 2D/3D registration called stochastic rank correlation (SRC). SRC is characterized by the fact that differences in image intensity do not influence the registration result; it therefore combines the numerical advantages of cross correlation (CC)-type merit functions with the flexibility of mutual-information-type merit functions. The basic idea is that registration is achieved on a random subset of the image, which allows for an efficient computation of Spearman’s rank correlation coefficient. This measure is, by nature, invariant to monotonic intensity transforms in the images under comparison, which renders it an ideal solution for intramodal images acquired at different energy levels as encountered in intrafractional kV imaging in image-guided radiotherapy. Initial evaluation was undertaken using a 2D/3D registration reference image dataset of a cadaver spine. Even with no radiometric calibration, SRC shows a significant improvement in robustness and stability compared to CC. Pattern intensity, another merit function that was evaluated for comparison, gave rather poor results due to its limited convergence range. The time required for SRC with 5% image content compares well to the other merit functions; increasing the image content does not significantly influence the algorithm accuracy. The authors conclude that SRC is a promising measure for 2D/3D registration in IGRT and image-guided therapy in general.

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## Higher-Rank Correlation NMR Spectra with Spectral Moment Filtering

Fonte: PubMed
Publicador: PubMed

Tipo: Artigo de Revista Científica

Publicado em 11/03/2010
EN

Relevância na Pesquisa

46.23%

Higher-rank correlation spectroscopy is introduced as an alternative to 3D Fourier-transform (FT) NMR spectroscopy for resonance assignment and molecular structure determination. The method combines standard 2D FT spectra that share a common frequency dimension, such as a 2D 13C-1H HSQC and a 2D 1H-1H TOCSY spectrum, and constructs higher-rank correlation spectra with ultra-high spectral resolution. Spectral overlap along a common dimension, in particular the 1H dimension, is addressed by a spectral filtering method, which identifies mismatches between the 1st and 2nd moments of cross-peak profiles. The method, which provides a substantial speed-up over traditional 3D FT spectroscopy while effectively suppressing false peaks, is demonstrated for the triple-rank 13C-1H HSQC-TOCSY spectrum of a cyclic decapeptide with different mixing times. Higher-rank correlation spectroscopy is usefully applicable to the analysis of a wide range of NMR spectra of synthetic and natural products.

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## Efficient implementation of the rank correlation merit function for 2D/3D registration

Fonte: PubMed
Publicador: PubMed

Tipo: Artigo de Revista Científica

EN

Relevância na Pesquisa

46.28%

A growing number of clinical applications using 2D/3D registration have been presented recently. Usually, a digitally reconstructed radiograph is compared iteratively to an x-ray image of the known projection geometry until a match is achieved, thus providing six degrees of freedom of rigid motion which can be used for patient setup in image-guided radiation therapy or computer-assisted interventions. Recently, stochastic rank correlation, a merit function based on Spearman's rank correlation coefficient, was presented as a merit function especially suitable for 2D/3D registration. The advantage of this measure is its robustness against variations in image histogram content and its wide convergence range. The considerable computational expense of computing an ordered rank list is avoided here by comparing randomly chosen subsets of the DRR and reference x-ray. In this work, we show that it is possible to omit the sorting step and to compute the rank correlation coefficient of the full image content as fast as conventional merit functions. Our evaluation of a well-calibrated cadaver phantom also confirms that rank correlation-type merit functions give the most accurate results if large differences in the histogram content for the DRR and the x-ray image are present.

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## Immunoradiometric detection of pS2 and total cathepsin D in primary breast cancer biopsies: their correlation with steroid receptors.

Fonte: PubMed
Publicador: PubMed

Tipo: Artigo de Revista Científica

Publicado em /03/1994
EN

Relevância na Pesquisa

36.2%

Commercially available immunoradiometric assays were used for pS2 and total cathepsin D determination in the cytosol fraction obtained from 266 primary breast cancers. We show that pS2 and cathepsin D values were significantly associated (Spearman's rank correlation: P < 0.0001) in tumours from lymph node-positive patients (N+), while such association did not reach significance in tumours taken from patients with negative lymph nodes (N-). Moreover, cathepsin D concentrations in pS2-rich tumours (pS2 above the median value, 5 ng mg-1 protein) were significantly higher (Mann-Whitney-Wilcoxon's rank-sum test: P = 0.00001) than those obtained in the samples expressing less than 5 ng of pS2 per mg of protein. pS2 was also correlated to both the oestrogen receptor (ER) (Spearman's rank correlation: P < 0.0001) and the progesterone receptor (PR) (Spearman's rank correlation: P = 0.022). No significant differences in the expression of pS2 and cathepsin D taken from N+ and N- patients were found. Furthermore, no significant differences in pS2 and cathepsin D expression were obtained by stratifying tumours on the basis of their size (T). pS2 and cathepsin D values obtained in ER-positive/PR-positive tumours did not significantly differ from the values obtained in ER-positive/PR-negative and in ER-negative/PR-positive tumours. We conclude that pS2 could have a role in cathepsin D expression...

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## Possible Causes of Long Range Dependence in the Brazilian Stock Market

Fonte: Physica A
Publicador: Physica A

Tipo: Artigo de Revista Científica
Formato: Texto

EN

Relevância na Pesquisa

45.97%

While the presence of long-range dependence in the asset returns seems to be a stylized fact,
the issue of arguing the possible causes of this phenomena is totally obscure. Trying to shed
light in this problem, we investigate the possible sources of the long-range dependence
phenomena in the Brazilian Stock Market. For this purpose, we employ a sample which
comprises stocks traded in the Brazilian financial market (BOVESPA Index). The Hurst
exponent here is considered as our measure of long-range dependence and it is evaluated by six
different methods. We have found evidence of statistically significant rank correlation between
specific variables of the Brazilian firms which subscribe stocks and the long-range dependence
phenomena present in these stocks.

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## On the Kendall Correlation Coefficient

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 06/07/2015

Relevância na Pesquisa

36.26%

In the present paper, we first discuss the Kendall rank correlation
coefficient. In continuous case, we define the Kendall rank correlation
coefficient in terms of the concomitants of order statistics, find the expected
value of the Kendall rank correlation coefficient and show that the later is
free of n. We also prove that in continuous case the Kendall correlation
coefficient converges in probability to its expected value. We then propose to
consider the expected value of the Kendall rank correlation coefficient as a
new theoretical correlation coefficient which can be an alternative to the
classical Pearson product-moment correlation coefficient. At the end of this
work we analyze illustrative examples.

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## Efficient Rank Reduction of Correlation Matrices

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

36.15%

Geometric optimisation algorithms are developed that efficiently find the
nearest low-rank correlation matrix. We show, in numerical tests, that our
methods compare favourably to the existing methods in the literature. The
connection with the Lagrange multiplier method is established, along with an
identification of whether a local minimum is a global minimum. An additional
benefit of the geometric approach is that any weighted norm can be applied. The
problem of finding the nearest low-rank correlation matrix occurs as part of
the calibration of multi-factor interest rate market models to correlation.; Comment: First version: 20 pages, 4 figures Second version [changed content]:
21 pages, 6 figures

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## Maximal Rank Correlation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/11/2015

Relevância na Pesquisa

46.22%

Based on the notion of maximal correlation, we introduce a new measure of
correlation between two different rankings of the same group of items. Our
measure captures various types of correlation detected in previous measures of
rank correlation like the Spearman correlation and the Kendall tau correlation.
We show that the maximal rank correlation satisfies the data processing and
tensorization properties (that make ordinary maximal correlation applicable to
problems in information theory). Furthermore, MRC is shown to be intimately
related to the FKG inequality. Finally, we pose the problem of the complexity
of the computation of this new measure. We make partial progress by giving a
simple but exponential-time algorithm for it.

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## Quotient correlation: A sample based alternative to Pearson's correlation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 07/04/2008

Relevância na Pesquisa

36.15%

The quotient correlation is defined here as an alternative to Pearson's
correlation that is more intuitive and flexible in cases where the tail
behavior of data is important. It measures nonlinear dependence where the
regular correlation coefficient is generally not applicable. One of its most
useful features is a test statistic that has high power when testing nonlinear
dependence in cases where the Fisher's $Z$-transformation test may fail to
reach a right conclusion. Unlike most asymptotic test statistics, which are
either normal or $\chi^2$, this test statistic has a limiting gamma
distribution (henceforth, the gamma test statistic). More than the common
usages of correlation, the quotient correlation can easily and intuitively be
adjusted to values at tails. This adjustment generates two new concepts--the
tail quotient correlation and the tail independence test statistics, which are
also gamma statistics. Due to the fact that there is no analogue of the
correlation coefficient in extreme value theory, and there does not exist an
efficient tail independence test statistic, these two new concepts may open up
a new field of study. In addition, an alternative to Spearman's rank
correlation, a rank based quotient correlation, is also defined. The advantages
of using these new concepts are illustrated with simulated data and a real data
analysis of internet traffic.; Comment: Published in at http://dx.doi.org/10.1214/009053607000000866 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org)

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## Monte Carlo error analyses of Spearman's rank test

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

36.16%

#Astrophysics - Instrumentation and Methods for Astrophysics#Physics - Data Analysis, Statistics and Probability#Statistics - Methodology

Spearman's rank correlation test is commonly used in astronomy to discern
whether a set of two variables are correlated or not. Unlike most other
quantities quoted in astronomical literature, the Spearman's rank correlation
coefficient is generally quoted with no attempt to estimate the errors on its
value. This is a practice that would not be accepted for those other
quantities, as it is often regarded that an estimate of a quantity without an
estimate of its associated uncertainties is meaningless. This manuscript
describes a number of easily implemented, Monte Carlo based methods to estimate
the uncertainty on the Spearman's rank correlation coefficient, or more
precisely to estimate its probability distribution.; Comment: Unubmitted manuscript (comments welcome); 5 pages; Code available at
https://github.com/PACurran/MCSpearman/; Updated with ASCL ID

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## PageRank and rank-reversal dependence on the damping factor

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/01/2012

Relevância na Pesquisa

36.28%

#Physics - Physics and Society#Computer Science - Social and Information Networks#Physics - Data Analysis, Statistics and Probability

PageRank (PR) is an algorithm originally developed by Google to evaluate the
importance of web pages. Considering how deeply rooted Google's PR algorithm is
to gathering relevant information or to the success of modern businesses, the
question of rank-stability and choice of the damping factor (a parameter in the
algorithm) is clearly important. We investigate PR as a function of the damping
factor d on a network obtained from a domain of the World Wide Web, finding
that rank-reversal happens frequently over a broad range of PR (and of d). We
use three different correlation measures, Pearson, Spearman, and Kendall, to
study rank-reversal as d changes, and show that the correlation of PR vectors
drops rapidly as d changes from its frequently cited value, $d_0=0.85$.
Rank-reversal is also observed by measuring the Spearman and Kendall rank
correlation, which evaluate relative ranks rather than absolute PR.
Rank-reversal happens not only in directed networks containing rank-sinks but
also in a single strongly connected component, which by definition does not
contain any sinks. We relate rank-reversals to rank-pockets and bottlenecks in
the directed network structure. For the network studied, the relative rank is
more stable by our measures around $d=0.65$ than at $d=d_0$.; Comment: 14 pages...

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## Spectral statistics of large dimensional Spearman's rank correlation matrix and its application

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

46.11%

Let $\mathbf{Q}=(Q_1,\ldots,Q_n)$ be a random vector drawn from the uniform
distribution on the set of all $n!$ permutations of $\{1,2,\ldots,n\}$. Let
$\mathbf{Z}=(Z_1,\ldots,Z_n)$, where $Z_j$ is the mean zero variance one random
variable obtained by centralizing and normalizing $Q_j$, $j=1,\ldots,n$. Assume
that $\mathbf {X}_i,i=1,\ldots ,p$ are i.i.d. copies of
$\frac{1}{\sqrt{p}}\mathbf{Z}$ and $X=X_{p,n}$ is the $p\times n$ random matrix
with $\mathbf{X}_i$ as its $i$th row. Then $S_n=XX^*$ is called the $p\times n$
Spearman's rank correlation matrix which can be regarded as a high dimensional
extension of the classical nonparametric statistic Spearman's rank correlation
coefficient between two independent random variables. In this paper, we
establish a CLT for the linear spectral statistics of this nonparametric random
matrix model in the scenario of high dimension, namely, $p=p(n)$ and $p/n\to
c\in(0,\infty)$ as $n\to\infty$. We propose a novel evaluation scheme to
estimate the core quantity in Anderson and Zeitouni's cumulant method in [Ann.
Statist. 36 (2008) 2553-2576] to bypass the so-called joint cumulant
summability. In addition, we raise a two-step comparison approach to obtain the
explicit formulae for the mean and covariance functions in the CLT. Relying on
this CLT...

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## Robust rank correlation based screening

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

46.17%

Independence screening is a variable selection method that uses a ranking
criterion to select significant variables, particularly for statistical models
with nonpolynomial dimensionality or "large p, small n" paradigms when p can be
as large as an exponential of the sample size n. In this paper we propose a
robust rank correlation screening (RRCS) method to deal with ultra-high
dimensional data. The new procedure is based on the Kendall \tau correlation
coefficient between response and predictor variables rather than the Pearson
correlation of existing methods. The new method has four desirable features
compared with existing independence screening methods. First, the sure
independence screening property can hold only under the existence of a second
order moment of predictor variables, rather than exponential tails or
alikeness, even when the number of predictor variables grows as fast as
exponentially of the sample size. Second, it can be used to deal with
semiparametric models such as transformation regression models and single-index
models under monotonic constraint to the link function without involving
nonparametric estimation even when there are nonparametric functions in the
models. Third, the procedure can be largely used against outliers and influence
points in the observations. Last...

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