Discriminant analysis for locally stationary processes

Kenji Sakiyama, Masanobu Taniguchi

    Research output: Contribution to journalArticle

    36 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

    Fingerprint

    Locally Stationary Processes
    Misclassification Probability
    Discriminant analysis
    Discriminant Analysis
    Robustness
    Nonstationary Processes
    Influence Function
    Spectral density
    Spectral Density
    Likelihood Ratio
    Stationary Process
    Stretch
    Numerical Study
    Time-varying
    Perturbation
    Converge
    Evaluate
    Zero
    Approximation
    Stationary process

    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, Probability and Uncertainty
    • Numerical Analysis
    • Statistics and Probability

    Cite this

    Discriminant analysis for locally stationary processes. / Sakiyama, Kenji; Taniguchi, Masanobu.

    In: Journal of Multivariate Analysis, Vol. 90, No. 2, 08.2004, p. 282-300.

    Research output: Contribution to journalArticle

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