ROBUST REGRESSION AND INTERPOLATION FOR TIME SERIES

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Abstract

Abstract. In this paper we shall consider the interpolation problem under the condition that the spectral density of a stationary process concerned is vaguely known (i.e., Huber's ε ‐contaminated model). Then we can get a minimax robust interpolator for the class of spectral densities S={ g:g(x)=(1‐ε)f(x)+εh(x)ε Ar Do, 0<ε<1}, where f(x) is a known spectral density and D0 is a certain class of spectral densities. Also we shall consider the time series regression problem under the condition that the residual spectral density is vaguely known. Then we can get a minimax robust regression coefficient estimate for the class of the residual spectral densities S.

Original languageEnglish
Pages (from-to)53-62
Number of pages10
JournalJournal of Time Series Analysis
Volume2
Issue number1
DOIs
Publication statusPublished - 1981
Externally publishedYes

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Keywords

  • interpolation
  • regression spectrum
  • robust estimation
  • spectral density
  • spectrum element
  • Stationary process
  • time series regression

ASJC Scopus subject areas

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

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