Development of Statistical Methods Using Predictive Inference and Entropy

摘要

In this Phase I study funded under the Small Business Innovation Research (SBIR) program, statistical methods are developed using the predictive inference and entropy approach. Previous recent research has derived entropy as the natural measure of model approximation error from the fundamental statistical principles of sufficiency and repeated sampling. In this study, the areas of nonnested multiple comparison, multivariable time series analysis, adaptive time series analysis of changing processes, and optimal small sample inference are investigated. Constrained maximum likelihood methods are developed for general nonnested multiple comparison. For the asymptotic optimality of these methods, a condition on the Fisher information and Hessian matrices must be satisfied. Applying these results to multivariate time series analysis, lower bounds are derived for the achievable accuracy of the estimated transfer function and spectral matrices. Markov and canonical variate analysis (CVA) provide a means of numerically and statistically stable model fitting of multivariable time series, and these methods provide a basis for modeling fitting time varying models of changing processes.