New efficient estimation and variable selection methods for semiparametric varying-coefficient partially linear models

Details New efficient estimation and variable selection methods for semiparametric varying-coefficient partially linear models New efficient estimation and variable selection methods for semiparametric varying-coefficient partially linear models

2011-03-08

arxiv.org/abs/1103.1525v1

Annals of Statistics 2011, Vol. 39, No. 1, 305-332

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/10-AOS842 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/10-AOS842

The complexity of semiparametric models poses new challenges to statistical inference and model selection that frequently arise from real applications. In this work, we propose new estimation and variable selection procedures for the semiparametric varying-coefficient partially linear model. We first study quantile regression estimates for the nonparametric varying-coefficient functions and the parametric regression coefficients. To achieve nice efficiency properties, we further develop a semiparametric composite quantile regression procedure. We establish the asymptotic normality of proposed estimators for both the parametric and nonparametric parts and show that the estimators achieve the best convergence rate. Moreover, we show that the proposed method is much more efficient than the least-squares-based method for many non-normal errors and that it only loses a small amount of efficiency for normal errors. In addition, it is shown that the loss in efficiency is at most 11.1% for estimating varying coefficient functions and is no greater than 13.6% for estimating parametric components. To achieve sparsity with high-dimensional covariates, we propose adaptive penalization methods for variable selection in the semiparametric varying-coefficient partially linear model and prove that the methods possess the oracle property. Extensive Monte Carlo simulation studies are conducted to examine the finite-sample performance of the proposed procedures. Finally, we apply the new methods to analyze the plasma beta-carotene level data.

Affiliated with

Also associated with

No associations

Rating

New efficient estimation and variable selection methods for semiparametric varying-coefficient partially linear models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with New efficient estimation and variable selection methods for semiparametric varying-coefficient partially linear models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and New efficient estimation and variable selection methods for semiparametric varying-coefficient partially linear models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-82614