• 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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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

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

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

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Zentralblatt MATH identifier

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


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.

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