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
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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 -