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Local Polynomial Variance-Function Estimation

In English

Författare

  • David Ruppert
  • Matt, P. Wand
  • Ulla Holst
  • Ola Hössjer

Summary, in English

The conditional variance function in a heteroscedastic, nonparametric regression model is estimated by linear smoothing of squared residuals. Attention is focused on local polynomial smoothers. Both the mean and variance functions are assumed to be smooth, but neither is assumed to be in a parametric family. The biasing effect of preliminary estimation of the mean is studied, and a degrees-of-freedom correction of bias is proposed. The corrected method is shown to be adaptive in the sense that the variance function can be estimated with the same asymptotic mean and variance as if the mean function were known. A proposal is made for using standard bandwidth selectors for estimating both the mean and variance functions. The proposal is illustrated with data from the LIDAR method of measuring atmospheric pollutants and from turbulence-model computations.

Publiceringsår

1997

Språk

Engelska

Sidor

262-273

Publikation/Tidskrift/Serie

Technometrics

Volym

39

Issue

3

Dokumenttyp

Artikel i tidskrift

Förlag

American Statistical Association

Ämne

  • Probability Theory and Statistics

Nyckelord

  • smoother matrix
  • regression
  • nonparametric
  • kernel smoothing
  • Bandwidth
  • heteroscedasticity

Status

Published

ISBN/ISSN/Övrigt

  • ISSN: 0040-1706