ON SPLINE SMOOTHING WITH AUTOCORRELATED ERRORS

Peter J. Diggle, Michael F. Hutchinson

Research output: Contribution to journalArticle

Abstract

The generalised cross‐validation criterion for choosing the degree of smoothing in spline regression is extended to accommodate an autocorrelated error sequence. It is demonstrated via simulation that the minimum generalised cross‐validation smoothing spline is an inconsistent estimator in the presence of autocorrelated errors and that ignoring even moderate autocorrelation structure can seriously affect the performance of the cross‐validated smoothing spline. The method of penalised maximum likelihood is used to develop an efficient algorithm for the case in which the autocorrelation decays exponentially. An application of the method to a published data‐set is described. The method does not require the data to be equally spaced in time.

Original languageEnglish (US)
Pages (from-to)166-182
Number of pages17
JournalAustralian Journal of Statistics
Volume31
Issue number1
DOIs
StatePublished - 1989
Externally publishedYes

Keywords

  • cross‐validation
  • non‐parametric regression
  • Splinesy
  • time series

ASJC Scopus subject areas

  • Statistics and Probability

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