Asymptotic distinction of counting processes
type: Item
instance of: scholarly article
title: Asymptotic distinction of counting processes
zbMATH Open document ID: 0803.62077
DOI: 10.1007/BF01057454
published in: Ukrainian Mathematical Journal
publication date: 1994-11-10T00:00:00Z
review text: The methods of statistics of counting processes based on the asymptotic properties of the likelihood ratio are intensively investigated. However, only the case of counting processes with continuous compensators has been studied in detail. This paper deals with the problem of testing two simple hypotheses for counting processes with increasing observation time. The study is based on the asymptotic properties of the likelihood ratio. We consider counting processes whose compensators may have discontinuities. A similar problem was investigated earlier for a special class of counting processes, namely, for the renewal processes [see the author and \textit{Munir al'Shakhf}, Ukr. Math. J. 44, No. 10, 1268-1275 (1992); translation from Ukr. Mat. Zh. 44, No. 10, 1383-1388 (1992; Zbl 0795.60019)].
Mathematics Subject Classification ID: 62M07
Mathematics Subject Classification ID: 62F05
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 652278
zbMATH Keywords: canonical representation
zbMATH Keywords: logarithm of the likelihood ratio
zbMATH Keywords: error of the second-kind
zbMATH Keywords: Neyman-Pearson test
zbMATH Keywords: process of local density
zbMATH Keywords: likelihood- ratio process
zbMATH Keywords: predictable process
zbMATH Keywords: law of large numbers
zbMATH Keywords: semimartingales
zbMATH Keywords: counting processes
zbMATH Keywords: simple hypotheses
zbMATH Keywords: compensators
zbMATH Keywords: discontinuities
author: Yu. N. Lin'kov
MaRDI profile type: Publication
cites work: Asymptotic discrimination between renewal processes
cites work: Multivariate point processes: predictable projection, Radon-Nikodym derivatives, representation of martingales
cites work: Q3800818
cites work: Q3943743
cites work: Q5511769
description: scientific article; zbMATH DE number 652278