Local asymptotic normality for linear homogeneous difference equations with non-Gaussian noise
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.
irreducible and contracting sets of matrices
scientific article; zbMATH DE number 1339513