DISCRIMINANT ANALYSIS FOR STATIONARY VECTOR TIME SERIES

Guoqiang Zhang, Masanobu Taniguchi

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)

Abstract

Abstract. In this paper, we shall consider the case where a stationary vector process {Xt} belongs to one of two categories described by two hypotheses π1 and π2. These hypotheses specify that {Xt} has spectral density matrices f(Λ) and g(Λ) under π1 and π2, respectively. Although Gaussianity of {Xt} is not assumed, we can formally make the Gaussian likelihood ratio (GLR) based on X(1),…X(T). Then an approximation I(f:g) of the GLR is given in terms of f(Λ) and g(Λ). If f(Λ) and g(Λ) are known, we can use I(f:g) as a classification statistic. It is shown that I(f:g) is a consistent classification criterion in the sense that the misclassification probabilities converge to zero as T→∝. When g is contiguous to f, we discuss non‐Gaussian robustness of I(f:g). A sufficient condition for the non‐Gaussian robustness will be given. Also a numerical example will be given.

Original languageEnglish
Pages (from-to)117-126
Number of pages10
JournalJournal of Time Series Analysis
Volume15
Issue number1
DOIs
Publication statusPublished - 1994 Jan
Externally publishedYes

Keywords

  • Vector linear process
  • classification criterion
  • innovation‐free
  • misclassification probability
  • non‐Gaussian robust
  • spectral density matrix

ASJC Scopus subject areas

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

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