A Review of the Research in Measurement Error Models

The measurement error models or EV(errors-in-variables) Models have been widely promoted in the field of statistics since 1877. According to the characteristics of the errors in variables, EV models can mainly be divided into three types: the additive model, the general measurement error model and berkson measurement error model. The emphases of researches in the EV models mainly focus on the effects of model estimation, hypothesis testing and model selection. In this paper, we concentrate on the research by conducted a systematic review of EV Models, in order to make a reference for researchers and practitioners.

[1]  Yanyuan Ma,et al.  Saddlepoint Test in Measurement Error Models , 2011 .

[2]  Cui Hengjian,et al.  On Parameter Estimation for Semi-linear Errors-in-Variables Models , 1998 .

[3]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[4]  Lung-fei Lee,et al.  Semiparametric estimation of nonlinear errors-in-variables models with validation study , 1995 .

[5]  Cheng Hsiao,et al.  CONSISTENT ESTIMATION FOR SOME NONLINEAR ERRORS-IN- VARIABLES MODELS , 1989 .

[6]  H. Koul,et al.  Regression model checking with Berkson measurement errors , 2008 .

[7]  Liqun Wang.  Estimation of nonlinear models with Berkson measurement errors , 2004 .

[8]  Hua Liang,et al.  Statistical inference for semiparametric varying-coefficient partially linear models with error-prone linear covariates , 2009, 0903.0499.

[9]  Han-Ying Liang,et al.  Empirical likelihood inference for partially time-varying coefficient errors-in-variables models , 2012 .

[10]  J. Shao,et al.  GMM in linear regression for longitudinal data with multiple covariates measured with error , 2010 .

[11]  Hengjian Cui,et al.  Empirical likelihood confidence region for parameter in the errors-in-variables models , 2003 .

[12]  David Ruppert,et al.  Additive Partial Linear Models with Measurement Errors. , 2008, Biometrika.

[13]  W. Härdle,et al.  Estimation in a semiparametric partially linear errors-in-variables model , 1999 .

[14]  Lixing Zhu,et al.  Empirical Likelihood Inference in Nonlinear Errors-in-Covariables Models With Validation Data , 2007 .

[15]  L. Stefanski,et al.  Corrected-loss estimation for quantile regression with covariate measurement errors. , 2012, Biometrika.

[16]  Liqun Wang.  Estimation of censored linear errors-in-variables models , 1998 .

[17]  R. Carroll,et al.  Quantile Regression With Measurement Error , 2009, Journal of the American Statistical Association.

[18]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[19]  Qihua Wang,et al.  Estimation of Partial Linear Error-in-Variables Models with Validation Data , 1999 .

[20]  J. N. K. Rao,et al.  Empirical likelihood-based inference in linear errors-in-covariables models with validation data , 2002 .

[21]  Runze Li,et al.  Variable Selection in Measurement Error Models. , 2010, Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability.

[22]  R. J. Adcock.  Note on the Method of Least Squares , 1877 .

[23]  Tong Li,et al.  Robust and consistent estimation of nonlinear errors-in-variables models , 2002 .

[24]  Hengjian Cui,et al.  Empirical Likelihood Confidence Region for Parameters in Semi‐linear Errors‐in‐Variables Models , 2006 .