• Journal of the Korean Statistical Society
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• v.32 no.1
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• pp.85-92
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• 2003

We consider the partially linear model E(Y) : X$^{t}$ $\beta$＋η(Z) when the X's are measured with additive error. The semiparametric likelihood estimation ignoring the measurement error gives inconsistent estimator for both $\beta$ and η(.). In this paper we suggest the SIMEX estimator for f to correct the bias induced by measurement error, and explore its properties. We show that the rational linear extrapolant is proper in extrapolation step in the sense that the SIMEX method under this extrapolant gives consistent estimator It is also shown that the SIMEX estimator is asymptotically equivalent to the semiparametric version of the usual parametric correction for attenuation suggested by Liang et al. (1999) A simulation study is given to compare two variance estimating methods for SIMEX estimator.

• Communications for Statistical Applications and Methods
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• v.26 no.1
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• pp.47-55
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• 2019

It is important to identify informative variables in high dimensional data analysis; however, it becomes a challenging task when covariates are contaminated by measurement error due to the bias induced by measurement error. In this article, we present a two-step approach for variable selection in the presence of measurement error. In the first step, we directly select important variables from the contaminated covariates as if there is no measurement error. We then apply, in the following step, orthogonal regression to obtain the unbiased estimates of regression coefficients identified in the previous step. In addition, we propose a modification of the two-step approach to further enhance the variable selection performance. Various simulation studies demonstrate the promising performance of the proposed method.