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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

Marcondes, Cintia Righetti
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%
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)...

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

Cobuci, Jaime Araújo; Euclydes, Ricardo Frederico; Costa, Claudio Napolis; Torres, Robledo de Almeida; Lopes, Paulo Sávio; Pereira, Carmen Silva
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%
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.

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

Ledic, Ivan Luz; Verneque, Rui da Silva; El Faro, Lenira; Tonhati, Humberto; Martinez, Mário Luiz; Oliveira, Mauro Dal Secco de; Costa, Cláudio Nápolis; Teodoro, Roberto Luiz; Fernandes, Leonardo de Oliveira
Fonte: Sociedade Brasileira de Zootecnia Publicador: Sociedade Brasileira de Zootecnia
Tipo: Artigo de Revista Científica Formato: 1964-1972
POR
Relevância na Pesquisa
45.97%
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...

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

Ortiz Peña, Carlos Dario; Queiroz, Sandra Aidar de; Fries, Luiz Alberto
Fonte: Sociedade Brasileira de Zootecnia Publicador: Sociedade Brasileira de Zootecnia
Tipo: Artigo de Revista Científica Formato: 93-100
POR
Relevância na Pesquisa
36.2%
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...

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

de Souza Gonçalves, Paulo; Bortoletto, Nelson; Cardinal, Átila Bento Beleti; Gouvêa, Lígia Regina Lima; da Costa, Reginaldo Brito; de Moraes, Mário Luiz Teixeira
Fonte: Universidade Estadual Paulista Publicador: Universidade Estadual Paulista
Tipo: Artigo de Revista Científica Formato: 758-764
ENG
Relevância na Pesquisa
56.12%
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...

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

Gonçalves,Paulo de Souza; Bortoletto,Nelson; Cardinal,Átila Bento Beleti; Gouvêa,Lígia Regina Lima; Costa,Reginaldo Brito da; Moraes,Mário Luiz Teixeira de
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%
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...

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

Cobuci,Jaime Araujo; Euclydes,Ricardo Frederico; Costa,Claudio Napolis; Torres,Robledo de Almeida; Lopes,Paulo Sávio; Pereira,Carmen Silva
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.

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

Birkfellner, Wolfgang; Stock, Markus; Figl, Michael; Gendrin, Christelle; Hummel, Johann; Dong, Shuo; Kettenbach, Joachim; Georg, Dietmar; Bergmann, Helmar
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.

Higher-Rank Correlation NMR Spectra with Spectral Moment Filtering

Bingol, Kerem; Salinas, Roberto K.; Brüschweiler, Rafael
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.

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

Figl, M; Bloch, C; Gendrin, C; Weber, C; Pawiro, S A; Hummel, J; Markelj, P; Pernuš, F; Bergmann, H; Birkfellner, W
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.

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

Marsigliante, S.; Biscozzo, L.; Correale, M.; Paradiso, A.; Leo, G.; Abbate, I.; Dragone, C. D.; Storelli, C.
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...

Possible Causes of Long Range Dependence in the Brazilian Stock Market

Cajueiro, Daniel Oliveira; Tabak, Benjamin Miranda
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.

On the Kendall Correlation Coefficient

Stepanov, Alexei
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.

Efficient Rank Reduction of Correlation Matrices

Grubisic, Igor; Pietersz, Raoul
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

Maximal Rank Correlation

Etesami, Omid; Gohari, Amin
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.

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

Zhang, Zhengjun
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)

Monte Carlo error analyses of Spearman's rank test

Curran, P. A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.16%
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

PageRank and rank-reversal dependence on the damping factor

Son, Seung-Woo; Christensen, Claire; Grassberger, Peter; Paczuski, Maya
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 23/01/2012
Relevância na Pesquisa
36.28%
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...

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

Bao, Zhigang; Lin, Liang-Ching; Pan, Guangming; Zhou, Wang
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...

Robust rank correlation based screening

Li, Gaorong; Peng, Heng; Zhang, Jun; Zhu, Lixing
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...