Asymptotic ancillarity and conditional inference for stochastic processes
type: Item
instance of: scholarly article
title: Asymptotic ancillarity and conditional inference for stochastic processes
zbMATH Open document ID: 0757.62013
author: Trevor Sweeting
published in: The Annals of Statistics
publication date: 1992-09-27T00:00:00Z
review text: The author aims to obtain limit theorems for the distributions of parameter estimators conditional on observed information. In greater generality, conditioning on any asymptotically ancillary statistic which includes data asymptotically equivalent to the observed information, is considered. The principal result obtained says that the conditional distributions of the randomly-normed score statistic and the randomly- normed maximum likelihood estimator, given such an asymptotically ancillary statistic, are asymptotically normal. Such a general statement has been rigorously formulated and proved in this paper. The theorems are stated under conditions that allow to apply them to inference from general stochastic processes and are relevant in particular for nonergodic models. The results can be considered as an extension of previous results of the same author [ibid. 14, 925-933 (1986; Zbl 0633.62084)] for supercritical branching processes. The mode of conditional convergence used in the present paper is weaker. An example illustrates the applicability and the importance of the results. The limit distributions derived can be used to improve the poor conditional performance of the unconditional confidence intervals.
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 62M99
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62M09
zbMATH DE Number: 61859
zbMATH Keywords: asymptotic conditional inference
zbMATH Keywords: asymptotic normality
zbMATH Keywords: asymptotically ancillary statistic
zbMATH Keywords: conditional distributions
zbMATH Keywords: randomly-normed score statistic
zbMATH Keywords: randomly-normed maximum likelihood estimator
zbMATH Keywords: nonergodic models
zbMATH Keywords: supercritical branching processes
zbMATH Keywords: conditional convergence
zbMATH Keywords: limit distributions
reviewed by: Spiridon Penev
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176348542
OpenAlex ID: W2073372451
DOI: 10.1214/AOS/1176348542
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description: scientific article; zbMATH DE number 61859