STATISTICAL METHODS USING PREDICTIVE INFERENCE AND ENTROPY DEVELOPMENT

PREDICTIVE INFERENCE GIVES A NATURAL AND GENERAL TREATMENT OF MANY STATISTICAL INFERENCE PROBLEMS WHICH ARE DIFFICULT TO HANDLE OR EVEN FORMULATE USING TRADITIONAL METHODS. RECENT RESULTS SHOW THAT NEGATIVE ENTROPY IS THE NATURAL MEASURE OF MODEL APPROXIMATION ERROR WHICH FOLLOWS FROM FUNDAMENTAL PRINCIPLES OF INFERENCE. THE OBJECTIVE OF THE PROPOSED RESEARCH FOR PHASE I IS TO FURTHER EXTEND AND DEVELOP SPECIFIC PREDICTIVE INFERENCE METHODS USING THE NEGATIVE ENTROPY MEASURE IN THE AREAS OF (1) MODEL BUILDING INVOLVING DETERMINATION OF PARAMETRIC MODEL STRUCTURE AND ORDER IN THE GENERAL CASE OF MULTIPLE NONNESTED ALTERNATIVES, (2) TIME SERIES MODELING AND FORECASTING INVOLVING DETERMINATION OF PARAMETRIC MODEL STRUCTURE, AND (3) SMALL SAMPLE INFERENCE FOR MULTIVARIATE DISTRIBUTIONS OF THE EXPONENTIAL FAMILY. PHASE II WILL INVOLVE FURTHER DEVELOPMENT OF PREDICTIVE INFERENCE METHODS FOR OTHER STATISTICAL INFERENCE PROBLEMS SUCH AS MISSING DATA, NONPARAMETRIC INFERENCE, EXPERIMENTAL DESIGN, ETC. PHASE III WILL INVOLVE THE DEVELOPMENT AND IMPLEMENTATION OF COMPUTATIONAL METHODS AND ALGORITHMS FOR USE IN A STATISTICAL SOFTWARE PACKAGE.