Boundary crossing probabilities for scan statistics and their applications to change-point detec\-tion
A review of recent results in change-point detection and in the associated boundary crossing problems is given. Likelihood statistics (LR) are considered. The sequence of observed random variables \(X_1,\ldots,X_n,\ldots\) is supposed being a Markov chain, taking values in \(\mathbb R^d\). \(X_t\) have a common specified distribution density \(f_0\) for \(t<\nu\) and another common distribution \(f_1\) for \(t\geq \nu\). Defining \(\xi_i= \log (f_1(X_i| X_{i-1}) /f_0(X_i| X_{i-1}))\) and \(S_{n,k}=\sum_{i=k+1}^n\), the LR statistics \(\max_{0\leq k \leq n}\;(n-k)g (S_{n,k}/(n-k))\) are considered for some smooth functions \(g\). Large deviation approximations are given. Detection procedures which are not too demanding in computational and memory requirements are motivated.
scientific article; zbMATH DE number 1960127