TY - JOUR

T1 - Nonparametric approach for discriminant analysis in time series

AU - Zhang, Guoqiang

AU - Taniguchi, Masanobu

PY - 1995/1/1

Y1 - 1995/1/1

N2 - In this paper, we shall consider the case where a stationary process {X(t)} belongs to one of two categories described by two hypotheses II1 and II2. These hypotheses specify that {X(t)} has spectral densities f1(λ) and f2(λ) under II1 and II2, respectively. It is known that the log-likelihood ratio based on Xn = [X(l),.,X(n)]' gives the optimal classification. Here we propose a new discriminant statistic Bα = eα(n, f2) – eα(n, f1), where eα(f1, f2) is the α-entropy of (A) with respect to f2(λ) and2(λ) is a nonparametric spectral estimator based on Xn. Then it is shown that the misclassification probabilities of Bα are asymptotically equivalent to those of I(f1, f2), an approximation of Gaussian log-likelihood ratio which is useful for discriminant analysis in time series. Furthermore Bα is shown to have peak robustness with respect to the spectral density. However I(f1, f2) does not have such property. Finally, simulation studies are given to confirm the theoretical results.

AB - In this paper, we shall consider the case where a stationary process {X(t)} belongs to one of two categories described by two hypotheses II1 and II2. These hypotheses specify that {X(t)} has spectral densities f1(λ) and f2(λ) under II1 and II2, respectively. It is known that the log-likelihood ratio based on Xn = [X(l),.,X(n)]' gives the optimal classification. Here we propose a new discriminant statistic Bα = eα(n, f2) – eα(n, f1), where eα(f1, f2) is the α-entropy of (A) with respect to f2(λ) and2(λ) is a nonparametric spectral estimator based on Xn. Then it is shown that the misclassification probabilities of Bα are asymptotically equivalent to those of I(f1, f2), an approximation of Gaussian log-likelihood ratio which is useful for discriminant analysis in time series. Furthermore Bα is shown to have peak robustness with respect to the spectral density. However I(f1, f2) does not have such property. Finally, simulation studies are given to confirm the theoretical results.

KW - Discriminant analysis

KW - log-likelihood ratio

KW - misclassification probability

KW - nonparametric spectral estimator

KW - peak robustness

KW - periodogram

KW - stationary processes

KW - α-entropy

UR - http://www.scopus.com/inward/record.url?scp=0010884797&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0010884797&partnerID=8YFLogxK

U2 - 10.1080/10485259508832637

DO - 10.1080/10485259508832637

M3 - Article

AN - SCOPUS:0010884797

VL - 5

SP - 91

EP - 101

JO - Journal of Nonparametric Statistics

JF - Journal of Nonparametric Statistics

SN - 1048-5252

IS - 1

ER -