DISCRIMINANT ANALYSIS FOR STATIONARY VECTOR TIME SERIES

Guoqiang Zhang, Masanobu Taniguchi

Research output: Contribution to journalArticle

21 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
Externally publishedYes

Fingerprint

Likelihood Ratio
Discriminant analysis
Discriminant Analysis
Time series
Spectral Density Matrix
Misclassification Probability
Robustness
Spectral density
Statistic
Statistics
Converge
Numerical Examples
Sufficient Conditions
Zero
Approximation
Likelihood ratio
Misclassification

Keywords

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

ASJC Scopus subject areas

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

Cite this

DISCRIMINANT ANALYSIS FOR STATIONARY VECTOR TIME SERIES. / Zhang, Guoqiang; Taniguchi, Masanobu.

In: Journal of Time Series Analysis, Vol. 15, No. 1, 1994, p. 117-126.

Research output: Contribution to journalArticle

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