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October 2009 A semiparametric model for cluster data
Wenyang Zhang, Jianqing Fan, Yan Sun
Ann. Statist. 37(5A): 2377-2408 (October 2009). DOI: 10.1214/08-AOS662

Abstract

In the analysis of cluster data, the regression coefficients are frequently assumed to be the same across all clusters. This hampers the ability to study the varying impacts of factors on each cluster. In this paper, a semiparametric model is introduced to account for varying impacts of factors over clusters by using cluster-level covariates. It achieves the parsimony of parametrization and allows the explorations of nonlinear interactions. The random effect in the semiparametric model also accounts for within-cluster correlation. Local, linear-based estimation procedure is proposed for estimating functional coefficients, residual variance and within-cluster correlation matrix. The asymptotic properties of the proposed estimators are established, and the method for constructing simultaneous confidence bands are proposed and studied. In addition, relevant hypothesis testing problems are addressed. Simulation studies are carried out to demonstrate the methodological power of the proposed methods in the finite sample. The proposed model and methods are used to analyse the second birth interval in Bangladesh, leading to some interesting findings.

Citation

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Wenyang Zhang. Jianqing Fan. Yan Sun. "A semiparametric model for cluster data." Ann. Statist. 37 (5A) 2377 - 2408, October 2009. https://doi.org/10.1214/08-AOS662

Information

Published: October 2009
First available in Project Euclid: 15 July 2009

zbMATH: 1173.62030
MathSciNet: MR2543696
Digital Object Identifier: 10.1214/08-AOS662

Subjects:
Primary: 62G08
Secondary: 62G10, 62G15

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 5A • October 2009
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