Large-Deviation Results for Discriminant Statistics of Gaussian Locally Stationary Processes. (4th July 2012)

• Record Type: Journal Article
• Authors: Hirukawa, Junichi
• Other Names: Tamaki Kenichiro Academic Editor.
• Is Part Of: Advances in decision sciences. Volume 2012(2012)
• Publication Date: 2012-07-04
• Subjects: Decision making -- Periodicals; Decision making; Electronic journals; Periodicals; 519
• DOI: 10.1155/2012/572919
• Languages: English
• ISSNs: 2090-3359

Abstract

Abstract : This paper discusses the large-deviation principle of discriminant statistics for Gaussian locally stationary processes. First, large-deviation theorems for quadratic forms and the log-likelihood ratio for a Gaussian locally stationary process with a mean function are proved. Their asymptotics are described by the large deviation rate functions. Second, we consider the situations where processes are misspecified to be stationary. In these misspecified cases, we formally make the log-likelihood ratio discriminant statistics and derive the large deviation theorems of them. Since they are complicated, they are evaluated and illustrated by numerical examples. We realize the misspecification of the process to be stationary seriously affecting our discrimination.