CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST 2012, 28(3) 319-330 DOI:      ISSN: 1001-4268 CN: 31-1256

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Partially Linear Models with Generalized Measurement Errors and Diverging Number of Parameters

Zhang Jun

School of Finance and Statistics, East China Normal University

Abstract��

We consider partially linear models in which
the linear covariate contains measurement errors, but instead an
observed surrogate that is linearly related to the unobserved
covariate. Moreover, the dimension of unobserved covariate diverges
with the sample size. We propose an estimation procedure and
establish the consistency and asymptotic normality property of
estimate. The rate of the divergent dimension is also investigated.
A simulation study and a real data are carried out to illustrate the
usefulness of the proposed method.

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