Efficient estimation of a semiparametric partially linear varying coefficient model

By Ibrahim A. Ahmad, S. Leelahanon, Qi Li. 2005

201 citations recorded by the source corpus.

In this paper we propose a general series method to estimate a semiparametric partially linear varying coefficient model. We establish the consistency and √n-normality property of the estimator of the finite-dimensional parameters of the model. We further show that, when the error is conditionally homoskedastic, this estimator is semiparametrically efficient in the sense that the inverse of the asymptotic variance of the estimator of the finite-dimensional parameter reaches the semiparametric efficiency bound of this model. A small-scale simulation is reported to examine the finite sample performance of the proposed estimator, and an empirical application is presented to illustrate the usefulness of the proposed method in practice. We also discuss how to obtain an efficient estimation result when the error is conditional heteroskedastic.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/571bc7e62fe6a1030cf54cb82fc1578783d0539c

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Citations in the corpus

Statistical Methods with Varying Coefficient Models. (2008, methodology): “Ahmad et al. (2005) used a general series method to estimate the semivarying coefficient model (2.”
Varying Coefficient Regression Models: A Review and New Developments (2015, result): “In Ahmad et al. (2005), the latter results were generalised to the partially linear varying coefficient model (2.4).”
Quantile regression in partially linear varying coefficient models (2009, methodology): “The PLVC models have been studied by Ahmad, Leelahanon and Li [1] and Fan and Huang [4] for cross-sectional data, and by Sun and Wu [23] and Fan, Huang and Li [5] for longitudinal data.”
A Mallows-Type Model Averaging Estimator for the Varying-Coefficient Partially Linear Model (2018, unknown): “Several studies, including Xia, Zhang, and Tong (2004) and Zhao and Xue (2010) mentioned above, have considered covariate selection for the VCPLM. Past research has shown that model selection underestimates the true variability of the model, and thereby results in overconfident © American Statistic”