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October 2015 Fused kernel-spline smoothing for repeatedly measured outcomes in a generalized partially linear model with functional single index
Fei Jiang, Yanyuan Ma, Yuanjia Wang
Ann. Statist. 43(5): 1929-1958 (October 2015). DOI: 10.1214/15-AOS1330

Abstract

We propose a generalized partially linear functional single index risk score model for repeatedly measured outcomes where the index itself is a function of time. We fuse the nonparametric kernel method and regression spline method, and modify the generalized estimating equation to facilitate estimation and inference. We use local smoothing kernel to estimate the unspecified coefficient functions of time, and use B-splines to estimate the unspecified function of the single index component. The covariance structure is taken into account via a working model, which provides valid estimation and inference procedure whether or not it captures the true covariance. The estimation method is applicable to both continuous and discrete outcomes. We derive large sample properties of the estimation procedure and show a different convergence rate for each component of the model. The asymptotic properties when the kernel and regression spline methods are combined in a nested fashion has not been studied prior to this work, even in the independent data case.

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Fei Jiang. Yanyuan Ma. Yuanjia Wang. "Fused kernel-spline smoothing for repeatedly measured outcomes in a generalized partially linear model with functional single index." Ann. Statist. 43 (5) 1929 - 1958, October 2015. https://doi.org/10.1214/15-AOS1330

Information

Received: 1 November 2014; Revised: 1 March 2015; Published: October 2015
First available in Project Euclid: 3 August 2015

zbMATH: 1327.62214
MathSciNet: MR3375872
Digital Object Identifier: 10.1214/15-AOS1330

Subjects:
Primary: 62G05

Keywords: B-spline , generalized linear model , Huntington’s disease , infinite dimension , logistic model , Semiparametric model , Single index model

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 5 • October 2015
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