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November 2018 Simultaneous nonparametric regression analysis of sparse longitudinal data
Hongyuan Cao, Weidong Liu, Zhou Zhou
Bernoulli 24(4A): 3013-3038 (November 2018). DOI: 10.3150/17-BEJ952

Abstract

Longitudinal data arise frequently in many scientific inquiries. To capture the dynamic relationship between longitudinal covariates and response, varying coefficient models have been proposed with point-wise inference procedures. This paper considers the challenging problem of asymptotically accurate simultaneous inference of varying coefficient models for sparse and irregularly observed longitudinal data via the local linear kernel method. The error and covariate processes are modeled as very general classes of non-Gaussian and non-stationary processes and are allowed to be statistically dependent. Simultaneous confidence bands (SCBs) with asymptotically correct coverage probabilities are constructed to assess the overall pattern and magnitude of the dynamic association between the response and covariates. A simulation based method is proposed to overcome the problem of slow convergence of the asymptotic results. Simulation studies demonstrate that the proposed inference procedure performs well in realistic settings and is favored over the existing point-wise and Bonferroni methods. A longitudinal dataset from the Chicago Health and Aging Project is used to illustrate our methodology.

Citation

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Hongyuan Cao. Weidong Liu. Zhou Zhou. "Simultaneous nonparametric regression analysis of sparse longitudinal data." Bernoulli 24 (4A) 3013 - 3038, November 2018. https://doi.org/10.3150/17-BEJ952

Information

Received: 1 March 2016; Revised: 1 January 2017; Published: November 2018
First available in Project Euclid: 26 March 2018

zbMATH: 06853272
MathSciNet: MR3779709
Digital Object Identifier: 10.3150/17-BEJ952

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

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