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DISCRIMINANT ANALYSIS FOR STATIONARY VECTOR TIME SERIES
Authors:Guoqiang  Zhang Masanobu  Taniguchi
Affiliation:Osaka University
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 π 1 and π 2. These hypotheses specify that { Xt } has spectral density matrices f (Λ) and g (Λ) under π 1 and π 2, 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.
Keywords:Vector linear process  classification criterion  spectral density matrix  misclassification probability  non-Gaussian robust  innovation-free
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