Bernoulli

  • Bernoulli
  • Volume 24, Number 4A (2018), 3013-3038.

Simultaneous nonparametric regression analysis of sparse longitudinal data

Hongyuan Cao, Weidong Liu, and Zhou Zhou

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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.

Article information

Source
Bernoulli, Volume 24, Number 4A (2018), 3013-3038.

Dates
Received: March 2016
Revised: January 2017
First available in Project Euclid: 26 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.bj/1522051232

Digital Object Identifier
doi:10.3150/17-BEJ952

Mathematical Reviews number (MathSciNet)
MR3779709

Zentralblatt MATH identifier
06853272

Keywords
local polynomial estimation maximum deviation nonparametric regression simultaneous confidence band sparse longitudinal data

Citation

Cao, Hongyuan; Liu, Weidong; Zhou, Zhou. Simultaneous nonparametric regression analysis of sparse longitudinal data. Bernoulli 24 (2018), no. 4A, 3013--3038. doi:10.3150/17-BEJ952. https://projecteuclid.org/euclid.bj/1522051232


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