Local asymptotic normality for linear homogeneous difference equations with non-Gaussian noise
type: Item
instance of: scholarly article
title: Local asymptotic normality for linear homogeneous difference equations with non-Gaussian noise
zbMATH Open document ID: 0933.60076
DOI: 10.1023/A:1021623714825
author: Andrius Jankunas
published in: Journal of Theoretical Probability
publication date: 2000-03-27T00:00:00Z
review text: The author establishes linear homogeneous stochastic difference equations of the form \(X_t=(A(\theta)+\eta_t)X_{t-1}\), \(t=1,2,\dots\), with random initial condition \(X_0\not =0,\) where \(X_t \in R^d, A(\theta)\) is a real \(d\times d\) matrix, \(\theta\) belongs to some open set in \(R^k, \eta_t\) are i.i.d. random matrices with mean 0. The work is devoted to the problem of estimation of drift parameter \(\theta.\) The local asymptotic normality of the family of distributions \(P_\theta^{(T)},\) corresponding to the realization \((X_1,\dots,X_T)\), as \(T\to \infty\), is proved. Properties of the Fisher's information matrix are studied. Examples are given.
Mathematics Subject Classification ID: 60H25
zbMATH DE Number: 1339513
zbMATH Keywords: stochastic difference equation
zbMATH Keywords: product of random matrices
zbMATH Keywords: local asymptotic normality
zbMATH Keywords: irreducible and contracting sets of matrices
reviewed by: Andriy Olenko
MaRDI profile type: Publication
full work available at URL: a:1021623714825
OpenAlex ID: W32146106
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description: scientific article; zbMATH DE number 1339513