Discriminant analysis for locally stationary processes

Kenji Sakiyama, Masanobu Taniguchi

Research output: Contribution to journalArticle

37 Citations (Scopus)

Abstract

In this paper, we discuss discriminant analysis for locally stationary processes, which constitute a class of non-stationary processes. Consider the case where a locally stationary process {Xt,T} belongs to one of two categories described by two hypotheses π1 and π2. Here T is the length of the observed stretch. These hypotheses specify that {Xt,T} has time-varying spectral densities f(u,λ) and g(u,λ) under π1 and π2, respectively. Although Gaussianity of {Xt,T} is not assumed, we use a classification criterion D(f:g), which is an approximation of the Gaussian likelihood ratio for {Xt,T} between π1 and π2. Then it is shown that D(f:g) is consistent, i.e., the misclassification probabilities based on D(f:g) converge to zero as T→∞. Next, in the case when g(u,λ) is contiguous to f(u,λ), we evaluate the misclassification probabilities, and discuss non-Gaussian robustness of D(f:g). Because the spectra depend on time, the features of non-Gaussian robustness are different from those for stationary processes. It is also interesting to investigate the behavior of D(f:g) with respect to infinitesimal perturbations of the spectra. Introducing an influence function of D(f:g), we illuminate its infinitesimal behavior. Some numerical studies are given.

Original languageEnglish
Pages (from-to)282-300
Number of pages19
JournalJournal of Multivariate Analysis
Volume90
Issue number2
DOIs
Publication statusPublished - 2004 Aug 1

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Keywords

  • Classification criterion
  • Influence function
  • Least favorable spectral density
  • Locally stationary vector process
  • Misclassification probability
  • Non-Gaussian robust
  • Time-varying spectral density matrix

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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