The Annals of Statistics

Fused kernel-spline smoothing for repeatedly measured outcomes in a generalized partially linear model with functional single index

Fei Jiang, Yanyuan Ma, and Yuanjia Wang

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 43, Number 5 (2015), 1929-1958.

Dates
Received: November 2014
Revised: March 2015
First available in Project Euclid: 3 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.aos/1438606849

Digital Object Identifier
doi:10.1214/15-AOS1330

Mathematical Reviews number (MathSciNet)
MR3375872

Zentralblatt MATH identifier
1327.62214

Subjects
Primary: 62G05: Estimation

Keywords
B-spline generalized linear model Huntington’s disease infinite dimension logistic model semiparametric model single index model

Citation

Jiang, Fei; Ma, Yanyuan; Wang, Yuanjia. Fused kernel-spline smoothing for repeatedly measured outcomes in a generalized partially linear model with functional single index. Ann. Statist. 43 (2015), no. 5, 1929--1958. doi:10.1214/15-AOS1330. https://projecteuclid.org/euclid.aos/1438606849


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Supplemental materials

  • Supplement to “Fused kernel-spline smoothing for repeatedly measured outcomes in a generalized partially linear model with functional single index”. We provide the comprehensive proofs of Theorems 1, 2 and 3 and additional lemmas which support the results.