Statistics and Its Interface

Volume 2 (2009)

Number 1

Empirical likelihood based inference for additive partial linear measurement error models

Pages: 83 – 90

DOI: http://dx.doi.org/10.4310/SII.2009.v2.n1.a8

Authors

Russ Hauser (Department of Environmental Health, Harvard School of Public Health, Boston, Mass., U.S.A.)

Hua Liang (Department of Biostatistics and Computational Biology, University of Rochester Medical Center, Rochester, N.Y., U.S.A.)

John D. Meeker (Department of Environmental Health Sciences, University of Michigan, Ann Arbor, Mich., U.S.A.)

Haiyan Su (Department of Biostatistics and Computational Biology, University of Rochester Medical Center, Rochester, N.Y., U.S.A.)

Sally W. Thurston (Department of Biostatistics and Computational Biology, University of Rochester Medical Center, Rochester, N.Y., U.S.A.)

Abstract

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.

Keywords

backfitting, correction-for-attenuation, coverage probability, error-prone, local linear regression, semiparamatric estimation, undersmoothing

2010 Mathematics Subject Classification

Primary 60Gxx, 62G10. Secondary 62G20.

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