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

Fei Jiang, Yanyuan Ma, Yuanjia Wang

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)1929-1958
Number of pages30
JournalAnnals of Statistics
Volume43
Issue number5
DOIs
StatePublished - Oct 1 2015

Fingerprint

Spline Smoothing
Partially Linear Model
Kernel Smoothing
Generalized Linear Model
Regression Splines
kernel
Local Smoothing
Kernel Regression
Generalized Estimating Equations
Nonparametric Methods
Kernel Methods
Covariance Structure
Linear Functional
Nonparametric Regression
B-spline
Estimate
Asymptotic Properties
Convergence Rate
Model
Valid

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

@article{fbc735e261d04f1ba514cea1a1b37156,
title = "Fused kernel-spline smoothing for repeatedly measured outcomes in a generalized partially linear model with functional single index",
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.",
author = "Fei Jiang and Yanyuan Ma and Yuanjia Wang",
year = "2015",
month = "10",
day = "1",
doi = "10.1214/15-AOS1330",
language = "English (US)",
volume = "43",
pages = "1929--1958",
journal = "Annals of Statistics",
issn = "0090-5364",
publisher = "Institute of Mathematical Statistics",
number = "5",

}

Fused kernel-spline smoothing for repeatedly measured outcomes in a generalized partially linear model with functional single index. / Jiang, Fei; Ma, Yanyuan; Wang, Yuanjia.

In: Annals of Statistics, Vol. 43, No. 5, 01.10.2015, p. 1929-1958.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Fused kernel-spline smoothing for repeatedly measured outcomes in a generalized partially linear model with functional single index

AU - Jiang, Fei

AU - Ma, Yanyuan

AU - Wang, Yuanjia

PY - 2015/10/1

Y1 - 2015/10/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84941211154&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84941211154&partnerID=8YFLogxK

U2 - 10.1214/15-AOS1330

DO - 10.1214/15-AOS1330

M3 - Article

C2 - 26283801

AN - SCOPUS:84941211154

VL - 43

SP - 1929

EP - 1958

JO - Annals of Statistics

JF - Annals of Statistics

SN - 0090-5364

IS - 5

ER -