Difference-based variance estimation in nonparametric regression with repeated measurement data

Wenlin Dai, Yanyuan Ma, Tiejun Tong, Lixing Zhu

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Over the past three decades, interest in cheap yet competitive variance estimators in nonparametric regression has grown tremendously. One family of estimators which has risen to meet the task is the difference-based estimators. Unlike their residual-based counterparts, difference-based estimators do not require estimating the mean function and are therefore popular in practice. This work further develops the difference-based estimators in the repeated measurement setting for nonparametric regression models. Three difference-based methods are proposed for the variance estimation under both balanced and unbalanced repeated measurement settings: the sample variance method, the partitioning method, and the sequencing method. Both their asymptotic properties and finite sample performance are explored. The sequencing method is shown to be the most adaptive while the sample variance method and the partitioning method are shown to outperform in certain cases.

Original languageEnglish (US)
Pages (from-to)1-20
Number of pages20
JournalJournal of Statistical Planning and Inference
Volume163
DOIs
StatePublished - Aug 1 2015

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Repeated Measurements
Variance Estimation
Nonparametric Regression
Estimator
Sample variance
Sequencing
Partitioning
Variance Estimator
Nonparametric Model
Nonparametric regression
Variance estimation
Asymptotic Properties
Regression Model

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Cite this

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Difference-based variance estimation in nonparametric regression with repeated measurement data. / Dai, Wenlin; Ma, Yanyuan; Tong, Tiejun; Zhu, Lixing.

In: Journal of Statistical Planning and Inference, Vol. 163, 01.08.2015, p. 1-20.

Research output: Contribution to journalArticle

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