Empirical Likelihood based Inference for Additive Partial Linear Measurement Error Models.

This paper considers statistical inference for additive partial linear models when the linear covariate is measured with error. To improve the accuracy of the normal approximation based confidence intervals, we develop an empirical likelihood based statistic, which is shown to be asymptotically chi-square distributed. We emphasize the finite-sample performance of the proposed method by conducting simulation experiments. The method is used to analyze the relationship between semen quality and phthalate exposure from an environment study.

[1]  O. Linton,et al.  A kernel method of estimating structured nonparametric regression based on marginal integration , 1995 .

[2]  Robert F. Herrick,et al.  Phthalate Exposure and Human Semen Parameters , 2003, Epidemiology.

[3]  V. V. Petrov.  Sums of Independent Random Variables , 1975 .

[4]  Art B. Owen,et al.  Empirical Likelihood for Linear Models , 1991 .

[5]  David Ruppert,et al.  A Root-n Consistent Backfitting Estimator for Semiparametric Additive Modeling , 1999 .

[6]  Song Xi Chen,et al.  Empirical Likelihood Confidence Intervals for Linear Regression Coefficients , 1994 .

[7]  Br Uce E. Ha,et al.  UNIFORM CONVERGENCE RATES FOR KERNEL ESTIMATION WITH DEPENDENT DATA , 2008 .

[8]  Jian Shi,et al.  Empirical Likelihood for Partially Linear Models , 2000 .

[9]  D. Ruppert,et al.  Measurement Error in Nonlinear Models , 1995 .

[10]  Jing Qin,et al.  Semi-empirical likelihood ratio confidence intervals for the difference of two sample means , 1994 .

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

[12]  David Ruppert,et al.  Fitting a Bivariate Additive Model by Local Polynomial Regression , 1997 .

[13]  Song Xi Chen,et al.  On the accuracy of empirical likelihood confidence regions for linear regression model , 1993 .

[14]  A. Calafat,et al.  Altered Semen Quality in Relation to Urinary Concentrations of Phthalate Monoester and Oxidative Metabolites , 2006, Epidemiology.

[15]  Bing-Yi Jing,et al.  Censored Partial Linear Models and Empirical Likelihood , 2001 .

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

[17]  C. J. Stone,et al.  Additive Regression and Other Nonparametric Models , 1985 .

[18]  Bing-Yi Jing,et al.  Empirical likelihood for partial linear models , 2003 .

[19]  Hua Liang,et al.  Partially Linear Models with Missing Response Variables and Error-prone Covariates. , 2007, Biometrika.

[20]  Empirical Likelihood in Partial Linear Error-in-Covariable Model with Censored Data , 2005 .

[21]  Antonia M. Calafat,et al.  Temporal Variability of Urinary Phthalate Metabolite Levels in Men of Reproductive Age , 2004, Environmental health perspectives.

[22]  J. Lawless,et al.  Empirical Likelihood and General Estimating Equations , 1994 .

[23]  Wolfgang Härdle,et al.  Partially Linear Models , 2000 .