The Annals of Statistics

A semiparametric model for cluster data

Wenyang Zhang, Jianqing Fan, and Yan Sun

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 37, Number 5A (2009), 2377-2408.

Dates
First available in Project Euclid: 15 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.aos/1247663759

Digital Object Identifier
doi:10.1214/08-AOS662

Mathematical Reviews number (MathSciNet)
MR2543696

Zentralblatt MATH identifier
1173.62030

Subjects
Primary: 62G08: Nonparametric regression
Secondary: 62G10: Hypothesis testing 62G15: Tolerance and confidence regions

Keywords
Varying-coefficient models local linear modeling cluster level variable cluster effect

Citation

Zhang, Wenyang; Fan, Jianqing; Sun, Yan. A semiparametric model for cluster data. Ann. Statist. 37 (2009), no. 5A, 2377--2408. doi:10.1214/08-AOS662. https://projecteuclid.org/euclid.aos/1247663759


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