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Impact of measurement errors on alternative predictors of lean meat proportion of lamb carcasses

Cadavez, Vasco
Fonte: Instituto Politécnico de Bragança Publicador: Instituto Politécnico de Bragança
Tipo: Conferência ou Objeto de Conferência
ENG
Relevância na Pesquisa
66.28%
The objectives of this study were to evaluate the impact of measurement errors on alternative predictors of lean meat proportion (LMP) of lamb carcasses. Ninety eight lambs (72 males and 26 females) of Churra Galega Bragançana breed were slaughtered, and carcasses were weighed (HCW) approximately 30 min after exsanguination. During carcasses quartering a caliper was used to perform tissue depth measurements, over the maximum depth of longissimus muscle (LM), between the 12th and 13th ribs (C12 ), and between the 3rd and 4th lumbar vertebrae (C3). The C12 and C3 measurements were contaminated with simulated measurement errors, and three distributions for random error were simulated: 1} random error with mean 0 and variance of 0.25 mm (E ~ N(0,0.25mm), 2) random error with mean 0 and variance of 0.50 mm (E ~ N(0,0.50mm)), and 3) random error with mean 0 and variance of 0.75 mm (E ~ N(0,0.75mm)). Simple and multiple linear regression models were developed using as independent variables the measured (original) and the biased C12 and C3 measurements as predictors of LMP. The coefficient of determination and the residual standard deviation were computed. This work shows that measurement errors of subcutaneous fat can have a high impact on the stability of models to predict the carcasses LMP. The subcutaneous fat measurements of higher magnitude are less sensitive to measurement errors...

Hypothesis testing in an errors-in-variables model with heteroscedastic measurement errors

CASTRO, Mario de; GALEA, Manuel; BOLFARINE, Heleno
Fonte: JOHN WILEY & SONS LTD Publicador: JOHN WILEY & SONS LTD
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
56.17%
In many epidemiological studies it is common to resort to regression models relating incidence of a disease and its risk factors. The main goal of this paper is to consider inference on such models with error-prone observations and variances of the measurement errors changing across observations. We suppose that the observations follow a bivariate normal distribution and the measurement errors are normally distributed. Aggregate data allow the estimation of the error variances. Maximum likelihood estimates are computed numerically via the EM algorithm. Consistent estimation of the asymptotic variance of the maximum likelihood estimators is also discussed. Test statistics are proposed for testing hypotheses of interest. Further, we implement a simple graphical device that enables an assessment of the model`s goodness of fit. Results of simulations concerning the properties of the test statistics are reported. The approach is illustrated with data from the WHO MONICA Project on cardiovascular disease. Copyright (C) 2008 John Wiley & Sons, Ltd.; FONDECYT (Fordo Nacional de Desarrollo Cientifico y Tecnologico, Chile); FONDECYT (Fordo Nacional de Desarrollo Cientifico y Tecnologico, Chile)[1070919]

Prediction with measurement errors in finite populations

Singer, Julio M.; Stanek, Edward J., III; Lencina, Viviana B.; Mery Gonzalez, Luz; Li, Wenjun; San Martino, Silvina
Fonte: ELSEVIER SCIENCE BV; AMSTERDAM Publicador: ELSEVIER SCIENCE BV; AMSTERDAM
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
46.3%
We address the problem of selecting the best linear unbiased predictor (BLUP) of the latent value (e.g., serum glucose fasting level) of sample subjects with heteroskedastic measurement errors. Using a simple example, we compare the usual mixed model BLUP to a similar predictor based on a mixed model framed in a finite population (FPMM) setup with two sources of variability, the first of which corresponds to simple random sampling and the second, to heteroskedastic measurement errors. Under this last approach, we show that when measurement errors are subject-specific, the BLUP shrinkage constants are based on a pooled measurement error variance as opposed to the individual ones generally considered for the usual mixed model BLUP. In contrast, when the heteroskedastic measurement errors are measurement condition-specific, the FPMM BLUP involves different shrinkage constants. We also show that in this setup, when measurement errors are subject-specific, the usual mixed model predictor is biased but has a smaller mean squared error than the FPMM BLUP which points to some difficulties in the interpretation of such predictors. (C) 2011 Elsevier By. All rights reserved.; Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq); Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq); Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP)...

A Study on the Foundations of the Occurrence of Errors in Subjective Measurements

Bispo, Carlos Alberto Ferreira; Cazarini, Edson Walmir
Fonte: Los Angeles Publicador: Los Angeles
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
46.27%
Background Due to the increasing need to better understand organizational elements, subjective measurements are gaining more and more space. Problem: What are the grounds to claim that subjective measurements allow for more possible measurement errors in relation to objective measurements? Purpose: To establish the necessary foundation to affirm that subjective measurements allow more measurement errors in relation to objective measurements. Methods: a comprehensive review of the literature on subjective and objective measurements was performed in order to establish the grounds of the problem outlined. Results: postulates on subjective measurements were elaborated and the main sources of subjective measurement errors, based on those postulates, were outlined. Conclusions: With the postulates and sources of errors outlined in the article, it was possible to formulate a theoretical framework that allowed us to better understand why subjective measurements are more subject to measurement errors in relation to objective measurements. Keywords:

Inferência em um modelo de regressão com resposta binária na presença de sobredispersão e erros de medição; Inference in a regression model with overdispersed binary response and measurement errors

Tieppo, Sandra Maria
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 15/02/2007 PT
Relevância na Pesquisa
56.13%
Modelos de regressão com resposta binária são utilizados na solução de problemas nas mais diversas áreas. Neste trabalho enfocamos dois problemas comuns em certos conjuntos de dados e que requerem técnicas apropriadas que forneçam inferências satisfatórias. Primeiro, em certas aplicações uma mesma unidade amostral é utilizada mais de uma vez, acarretando respostas positivamente correlacionadas, responsáveis por uma variância na variável resposta superior ao que comporta a distribuição binomial, fenômeno conhecido como sobredispersão. Por outro lado, também encontramos situações em que a variável explicativa contém erros de medição. É sabido que utilizar técnicas que desconsideram esses erros conduz a resultados inadequados (estimadores viesados e inconsistentes, por exemplo). Considerando um modelo com resposta binária, utilizaremos a distribuição beta-binomial para representar a sobredispersão. Os métodos de máxima verossimilhança, SIMEX, calibração da regressão e máxima pseudo-verossimilhança foram usados na estimação dos parâmetros do modelo, que são comparados através de um estudo de simulação. O estudo de simulação sugere que os métodos de máxima verossimilhança e calibração da regressão são melhores no sentido de correção do viés...

Modelos mistos para populações finitas com erros de medida endógenos e exógenos; Finite population mixed models with endogenous and exogenous measurement errors

Arenas, German Moreno
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 02/09/2009 PT
Relevância na Pesquisa
66.21%
Consideramos a predição ótima de valores latentes com base em dados sujeitos a erros de medida endógenos e exógenos, obtidos a partir de uma amostra aleatória de uma população finita. Consideramos o modelo misto para populações finitas (MMPF) com erros de medida exógenos e endógenos usando o enfoque proposto por Stanek et al. (2004) e Stanek & Singer (2004), e calculamos o melhor preditor linear não enviesado (BLUP) do valor latente da i-ésima unidade selecionada na amostra. Quando as variâncias endógenas são heterocedásticas, o preditor obtido sob o MMPF é diferente do preditor obtido sob o modelo misto usual, pois a constante de encolhimento depende da média das variâncias individuais. Utilizamos simulação para comparar o preditor obtido sob o modelo misto usual (utilizado conforme a interpretação usual) com o preditor obtido sob o MMPF, mostrando que apesar do primeiro ser enviesado, ele geralmente apresenta erro quadrático médio (EQM) menor (ou ligeiramente maior) do que aquele obtido sob o MMPF. Adicionalmente, mostramos como utilizar dois pacotes de \emph estatístico (Proc MIXED do SAS e lme(nlme) do R), construídos sob o modelo misto usual, para ajustar corretamente modelos em situações com erros exógenos e endógenos...

Modeling approach based on experimental results for prediction of measurement errors in energy meters

Gonçalves, Flávio A. S.; Canesin, Carlos A.; Pinto, João O. P.; Galotto Jr., Luigi G.; Godoy, Ruben B.
Fonte: Universidade Estadual Paulista Publicador: Universidade Estadual Paulista
Tipo: Conferência ou Objeto de Conferência Formato: 1255-1261
ENG
Relevância na Pesquisa
66.21%
This paper presents a general modeling approach to investigate and to predict measurement errors in active energy meters both induction and electronic types. The measurement error modeling is based on Generalized Additive Model (GAM), Ridge Regression method and experimental results of meter provided by a measurement system. The measurement system provides a database of 26 pairs of test waveforms captured in a real electrical distribution system, with different load characteristics (industrial, commercial, agricultural, and residential), covering different harmonic distortions, and balanced and unbalanced voltage conditions. In order to illustrate the proposed approach, the measurement error models are discussed and several results, which are derived from experimental tests, are presented in the form of three-dimensional graphs, and generalized as error equations. © 2009 IEEE.

Measurement errors in multivariate chemical data

Wentzell,Peter D.
Fonte: Sociedade Brasileira de Química Publicador: Sociedade Brasileira de Química
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/02/2014 EN
Relevância na Pesquisa
66.25%
Modern analytical measurements are commonly presented in the form of vectors (e.g., spectra) or higher order data structures such as matrices, and these are often subjected to multivariate data analysis strategies to extract information. One aspect of these measurements that is often poorly understood is the underlying nature of the measurement errors and how these affect the ability to obtain chemical information. This Account outlines some of the methods that can be used to characterize multivariate measurement errors and how this information can be used to improve the results of data analysis. Characterization includes general classifications of error, Fourier domain representations, and the error covariance matrix. The calculation and interpretation of error covariance and correlation matrices are illustrated using experimental measurements, and data analysis methods that make use of this error information are briefly reviewed. A simple example is presented to show how information about measurement errors allows for more effective extraction of meaningful chemical variance in the data.

Elimination of Systematic Mass Measurement Errors in Liquid Chromatography-Mass Spectrometry Based Proteomics using Regression Models and a priori Partial Knowledge of the Sample Content

Petyuk, Vladislav A.; Jaitly, Navdeep; Moore, Ronald J.; Ding, Jie; Metz, Thomas O.; Tang, Keqi; Monroe, Matthew E.; Tolmachev, Aleksey V.; Adkins, Joshua N.; Belov, Mikhail E.; Dabney, Alan R.; Qian, Wei-Jun; Camp, David G.; Smith, Richard D.
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
46.28%
The high mass measurement accuracy and precision available with recently developed mass spectrometers is increasingly used in proteomics analyses to confidently identify tryptic peptides from complex mixtures of proteins, as well as post-translational modifications and peptides from non-annotated proteins. To take full advantage of high mass measurement accuracy instruments it is necessary to limit systematic mass measurement errors. It is well known that errors in the measurement of m/z can be affected by experimental parameters that include e.g., outdated calibration coefficients, ion intensity, and temperature changes during the measurement. Traditionally, these variations have been corrected through the use of internal calibrants (well-characterized standards introduced with the sample being analyzed). In this paper we describe an alternative approach where the calibration is provided through the use of a priori knowledge of the sample being analyzed. Such an approach has previously been demonstrated based on the dependence of systematic error on m/z alone. To incorporate additional explanatory variables, we employed multidimensional, nonparametric regression models, which were evaluated using several commercially available instruments. The applied approach is shown to remove any noticeable biases from the overall mass measurement errors...

Spatial Linear Mixed Models with Covariate Measurement Errors

Li, Yi; Tang, Haicheng; Lin, Xihong
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em //2009 EN
Relevância na Pesquisa
46.26%
Spatial data with covariate measurement errors have been commonly observed in public health studies. Existing work mainly concentrates on parameter estimation using Gibbs sampling, and no work has been conducted to understand and quantify the theoretical impact of ignoring measurement error on spatial data analysis in the form of the asymptotic biases in regression coefficients and variance components when measurement error is ignored. Plausible implementations, from frequentist perspectives, of maximum likelihood estimation in spatial covariate measurement error models are also elusive. In this paper, we propose a new class of linear mixed models for spatial data in the presence of covariate measurement errors. We show that the naive estimators of the regression coefficients are attenuated while the naive estimators of the variance components are inflated, if measurement error is ignored. We further develop a structural modeling approach to obtaining the maximum likelihood estimator by accounting for the measurement error. We study the large sample properties of the proposed maximum likelihood estimator, and propose an EM algorithm to draw inference. All the asymptotic properties are shown under the increasing-domain asymptotic framework. We illustrate the method by analyzing the Scottish lip cancer data...

Prediction with measurement errors in finite populations

Singer, Julio M; Stanek, Edward J; Lencina, Viviana B; González, Luz Mery; Li, Wenjun; Martino, Silvina San
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em 01/02/2012 EN
Relevância na Pesquisa
46.3%
We address the problem of selecting the best linear unbiased predictor (BLUP) of the latent value (e.g., serum glucose fasting level) of sample subjects with heteroskedastic measurement errors. Using a simple example, we compare the usual mixed model BLUP to a similar predictor based on a mixed model framed in a finite population (FPMM) setup with two sources of variability, the first of which corresponds to simple random sampling and the second, to heteroskedastic measurement errors. Under this last approach, we show that when measurement errors are subject-specific, the BLUP shrinkage constants are based on a pooled measurement error variance as opposed to the individual ones generally considered for the usual mixed model BLUP. In contrast, when the heteroskedastic measurement errors are measurement condition-specific, the FPMM BLUP involves different shrinkage constants. We also show that in this setup, when measurement errors are subject-specific, the usual mixed model predictor is biased but has a smaller mean squared error than the FPMM BLUP which point to some difficulties in the interpretation of such predictors.

Correcting the Errors : A Note on Volatility Forecast Evaluation Based on High-Frequency Data and Realized Volatilities

ANDERSEN, Torben G.; BOLLERSLEV, Tim; MEDDAHI, Nour
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Artigo de Revista Científica Formato: 158041 bytes; application/pdf
Relevância na Pesquisa
56.03%
This note develops general model-free adjustment procedures for the calculation of unbiased volatility loss functions based on practically feasible realized volatility benchmarks. The procedures, which exploit the recent asymptotic distributional results in Barndorff-Nielsen and Shephard (2002a), are both easy to implement and highly accurate in empirically realistic situations. On properly accounting for the measurement errors in the volatility forecast evaluations reported in Andersen, Bollerslev, Diebold and Labys (2003), the adjustments result in markedly higher estimates for the true degree of return-volatility predictability.; Cette note développe des méthodes d’ajustement, sans spécifier le modèle, qui corrigent le biais induit par les erreurs de mesures de la volatilité dans la mesure de performance des méthodes de prévision de la volatilité. Les procédures, qui utilisent la récente théorie asymptotique de Barndorff-Nielsen et Shephard (2002a), sont faciles à mettre en oeuvre et très performantes dans les situations empiriques usuelles. En particulier, la prise en compte des erreurs de mesures dans les procédures de prévision de Andersen, Bollerslev, Diebold et Labys (2003), amène à des performances de prévision de la volatilité très élevées.

Earnings Mobility and Measurement Error : A Pseudo-Panel Approach

Antman, Francisca; McKenzie, David J.
Fonte: World Bank, Washington, DC Publicador: World Bank, Washington, DC
Relevância na Pesquisa
56.08%
The degree of mobility in incomes is often seen as an important measure of the equality of opportunity in a society and of the flexibility and freedom of its labor market. But estimation of mobility using panel data is biased by the presence of measurement error and non-random attrition from the panel. This paper shows that dynamic pseudo-panel methods can be used to consistently estimate measures of absolute and conditional mobility in the presence of non-classical measurement errors. These methods are applied to data on earnings from a Mexican quarterly rotating panel. Absolute mobility in earnings is found to be very low in Mexico, suggesting that the high level of inequality found in the cross-section will persist over time. However, the paper finds conditional mobility to be high, so that households are able to recover quickly from earnings shocks. These findings suggest a role for policies which address underlying inequalities in earnings opportunities.

What Does Variation in Survey Design Reveal about the Nature of Measurement Errors in Household Consumption?

Gibson, John; Beegle, Kathleen; De Weerdt, Joachim; Friedman, Jed
Fonte: World Bank, Washington, DC Publicador: World Bank, Washington, DC
EN_US
Relevância na Pesquisa
66.26%
This paper uses data from eight different consumption questionnaires randomly assigned to 4,000 households in Tanzania to obtain evidence on the nature of measurement errors in estimates of household consumption. While there are no validation data, the design of one questionnaire and the resources put into its implementation make it likely to be substantially more accurate than the others. Comparing regressions using data from this benchmark design with results from the other questionnaires shows that errors have a negative correlation with the true value of consumption, creating a non-classical measurement error problem for which conventional statistical corrections may be ineffective.

Benefit Incidence with Incentive Effects, Measurement Errors and Latent Heterogeneity

Ravallion, Martin; Chen, Shaohua
Fonte: World Bank, Washington, DC Publicador: World Bank, Washington, DC
Tipo: Publications & Research :: Policy Research Working Paper; Publications & Research
ENGLISH; EN_US
Relevância na Pesquisa
66.25%
Empirical studies of tax and benefit incidence routinely ignore behavioral responses and measurement errors. This paper offers an econometric method of estimating the mean benefit withdrawal rate (marginal tax rate) allowing for incentive effects, measurement errors, and correlated latent heterogeneity in incidence. Under the method's identifying assumptions, a feasible instrumental variables estimator corrects for incentive effects and measurement errors, and provides a bound for the true value when there is correlated incidence heterogeneity. A case study for a large cash transfer program in China indicates that past methods of assessing benefit incidence using either nominal official rates or raw tabulations from survey data are deceptive. The program entails a nominal 100 percent benefit withdrawal rate -- a poverty trap. However, the paper finds that the actual rate is much lower, and clearly too low in the light of the literature on optimal income taxation. The paper discusses likely reasons based on the qualitative observations.

"Uma aplicação industrial de regressão binária com erros na variável explicativa" ; "An industrial application of binary regression with errors-in-variable explanatory"

Favari, Daniel Fernando de
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 22/06/2006 PT
Relevância na Pesquisa
56.21%
Neste trabalho, aplicamos um modelo de regressão binária com erros de medição na variável explicativa para analisar sistemas de medição do tipo atributo. Para isto, utilizamos o modelo logístico com erros na variável, para o qual obtemos as estimativas de máxima verossimilhança via o algoritmo EM e a matriz de informação de Fisher observada. Além disso, fizemos um estudo de simulação para compararmos o método analítico e os modelos logístico sem erros na variável (ingênuo) e logístico com erros na variável. Finalmente, aplicamos nossa metodologia para avaliarmos um sistema de medição passa/não passa da maior montadora de motores Diesel (MWM International).; In this work, we apply a study of binary regression model with errors-in-variable to analyze attributive measurement systems. For this, we use the logistic model with errors-in-variable to obtain parameter estimates of maximum likelihood through EM algorithm and the observed Fisher information matrix. In addition we do a simulation study to compare analytic method and the logistic model with and without measurement errors-in-variable. Finally, we apply our methodology to evaluate a attributive measurement system for the largest Diesel motor company of the world (MWM International).

Measurement Errors of Expected Returns Proxies and the Implied Cost of Capital

Wang, Charles Chang-Yi
Fonte: Harvard University Publicador: Harvard University
Tipo: Research Paper or Report
EN_US
Relevância na Pesquisa
66.31%
This paper presents a methodology to study implied cost of capital's (ICC) measurement errors, which are relatively unstudied empirically despite ICCs' popularity as proxies of expected returns. By applying it to the popular implementation of ICCs of Gebhardt, Lee, and Swaminathan (2001) (GLS), I show that the methodology is useful for explaining the variation in GLS measurement errors. I document the first direct empirical evidence that ICC measurement errors can be persistent, can be associated with firms' risk or growth characteristics, and thus confound regression inferences on expected returns. I also show that GLS measurement errors and the spurious correlations they produce are driven not only by analysts' systematic forecast errors but also by functional form assumptions. This finding suggests that correcting for the former alone is unlikely to fully resolve these measurement-error issues. To make robust inferences on expected returns, ICC regressions should be complemented by realized-returns regressions.

Subcutaneous fat depth magnitude influences its measurement errors: a simulation study

Cadavez, Vasco; Amaro, Rufino; Fonseca, António
Fonte: EUROSIS-ETI. Escola Superior Agrária de Bragança, CIMO Publicador: EUROSIS-ETI. Escola Superior Agrária de Bragança, CIMO
Tipo: Conferência ou Objeto de Conferência
ENG
Relevância na Pesquisa
56.26%
The objectives of this study were to evaluate the impact of proportional and absolute errors on subcutaneous fat depth (SFD) measurements, and the effects on the stability of models to predict the lean meat proportion (LMP) of lamb carcasses. Ninety eight lambs (72 males and 26 females) of Churra Galega Bragançana breed were slaughtered, and carcasses were weighed (HCW) approximately 30 min after exsanguination. During carcasses quartering a caliper was used to perform SFD measurements, over the maximum depth of longissimus muscle (LM), between the 12th and 13th ribs (C12), and between the 3rd and 4th lumbar vertebrae (C3). A computer program was written in order to simulate measurement errors for C12 and C3 measurements. Two scenarios were simulated, and C12 and C3 were contaminated with: 1) proportional errors of 5, 10, and 15%, and 2) absolute errors of 0.25, 0.50, and 0.75 mm. Simple and multiple linear models to predict LMP were developed using as independent variables: 1) the measured (original) SFD measurements, and 2) the biased SFD measurements. The coefficient of determination ( ) and the residual SD (RSD) were computed. Our study demonstrates that measurement errors can have a high impact on the SFD measurements, and on models stability. We conclude that SFD measurements of higher magnitude should be preferred as predictors of LMP since they are less influenced by measurement errors...

Linear Regression for Astronomical Data with Measurement Errors and Intrinsic Scatter

Akritas, Michael G.; Bershady, Matthew A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 01/05/1996
Relevância na Pesquisa
46.34%
Two new methods are proposed for linear regression analysis for data with measurement errors. Both methods are designed to accommodate intrinsic scatter in addition to measurement errors. The first (BCES) is a direct extension of the ordinary least squares (OLS) estimator to allow for measurement errors. It is quite general, allowing a) for measurement errors on both variables, b) the measurement errors for the two variables to be dependent, c) the magnitudes of the measurement errors to depend on the measurements, and d) other `symmetric' lines such as the bisector and the orthogonal regression can be constructed. The second method is a weighted least squares (WLS) estimator, which applies only in the case where the `independent' variable is measured without error and the magnitudes of the measurement errors on the 'dependent' variable are independent from the measurements. Several applications are made to extragalactic astronomy: The BCES method, when applied to data describing the color-luminosity relations for field galaxies, yields significantly different slopes than OLS and other estimators used in the literature. Simulations with artificial data sets are used to evaluate the small sample performance of the estimators. Unsurprisingly...

Test-cost-sensitive attribute reduction of data with normal distribution measurement errors

Zhao, Hong; Min, Fan; Zhu, William
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.28%
The measurement error with normal distribution is universal in applications. Generally, smaller measurement error requires better instrument and higher test cost. In decision making based on attribute values of objects, we shall select an attribute subset with appropriate measurement error to minimize the total test cost. Recently, error-range-based covering rough set with uniform distribution error was proposed to investigate this issue. However, the measurement errors satisfy normal distribution instead of uniform distribution which is rather simple for most applications. In this paper, we introduce normal distribution measurement errors to covering-based rough set model, and deal with test-cost-sensitive attribute reduction problem in this new model. The major contributions of this paper are four-fold. First, we build a new data model based on normal distribution measurement errors. With the new data model, the error range is an ellipse in a two-dimension space. Second, the covering-based rough set with normal distribution measurement errors is constructed through the "3-sigma" rule. Third, the test-cost-sensitive attribute reduction problem is redefined on this covering-based rough set. Fourth, a heuristic algorithm is proposed to deal with this problem. The algorithm is tested on ten UCI (University of California - Irvine) datasets. The experimental results show that the algorithm is more effective and efficient than the existing one. This study is a step toward realistic applications of cost-sensitive learning.; Comment: This paper has been withdrawn by the author due to the error of the title