Global statistical information in exponential experiments and selection of exponential models
The paper deals with a classical statistical experiment producing a sequence of iid observations \(X_1,\ldots ,X_n\) with distribution \(P_{\vartheta _0}\) from an exponential family of distributions. The concept of global statistical information \(I_{\vartheta _0}(S)\) is applied in this context. The global information has been introduced in a paper of \textit{I. Vajda} [Global statistical information, likelihood ratio test and maximum likelihood estimators. Kybernetika, submitted 1997]. It evaluates the amount of evidence per observation in favour of the hypothesis that the true parameter \(\vartheta _0\) lies in a given subset \(S\) of the parametric space \(\Theta\). Explicit formulas are given for common exponential families of distributions. One of the main results of the paper shows that the generalized likelihood ratio test procedure of model selection can be replaced by an information procedure that is based just on the global information. This procedure is compared with that one based on the Akaike criterion using simulations in classical regression models.
scientific article; zbMATH DE number 1450139
scientific article