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Semiparametric partially linear regression models for functional data

Authors
Journal
Journal of Statistical Planning and Inference
0378-3758
Publisher
Elsevier
Volume
142
Issue
9
Identifiers
DOI: 10.1016/j.jspi.2012.03.004
Keywords
  • Longitudinal Data
  • Functional Data
  • Semiparametric Partially Linear Regression Models
  • Asymptotic Normality

Abstract

Abstract In the context of longitudinal data analysis, a random function typically represents a subject that is often observed at a small number of time point. For discarding this restricted condition of observation number of each subject, we consider the semiparametric partially linear regression models with mean function x⊤β + g(z), where x and z are functional data. The estimations of β and g(z) are presented and some asymptotic results are given. It is shown that the estimator of the parametric component is asymptotically normal. The convergence rate of the estimator of the nonparametric component is also obtained. Here, the observation number of each subject is completely flexible. Some simulation study is conducted to investigate the finite sample performance of the proposed estimators.

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