Error variance estimation via least squares for small sample nonparametric regression

Chun Gun Park, Inyoung Kim, Yung Seop Lee

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

In this paper we explore statistical properties of some difference-based approaches to estimate an error variance for small sample based on nonparametric regression which satisfies Lipschitz condition. Our study is motivated by Tong and Wang (2005), who estimated error variance using a least squares approach. They considered the error variance as the intercept in a simple linear regression which was obtained from the expectation of their lag-. k Rice estimator. Their variance estimators are highly dependent on the setting of a regressor and weight of their simple linear regression. Although this regressor and weight can be varied based on the characteristic of an unknown nonparametric mean function, Tong and Wang (2005) have used a fixed regressor and weight in a large sample and gave no indication of how to determine the regressor and the weight. In this paper, we propose a new approach via local quadratic approximation to determine this regressor and weight. Using our proposed regressor and weight, we estimate the error variance as the intercept of simple linear regression using both ordinary least squares and weighted least squares. Our approach applies to both small and large samples, while most existing difference-based methods are appropriate solely for large samples. We compare the performance of our approach with other existing approaches using extensive simulation study. The advantage of our approach is demonstrated using a real data set.

Original languageEnglish
Pages (from-to)2369-2385
Number of pages17
JournalJournal of Statistical Planning and Inference
Volume142
Issue number8
DOIs
StatePublished - Aug 2012

Keywords

  • Difference-based estimator
  • Least squares
  • Lipschitz condition
  • Nonparametric regression
  • Residual variance

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