Theory and application of information extraction in mathematical statistics

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In this research, we investigated the theory of information extraction in mathematical statistics and applied the results to various kinds of practical data-set. 11 special topics were selected and research sympojiums were held on each topic. As a result, new theories and methodologies were developed and useful knowledges were obtained in many practical fields. Statistical software were also constructed. Through discussions in sympojiums and meetings, further problems were pointed out. Main results obtained in 11 sympojiums were as follows :(1) Development of the theories and methodologies for analyzing complicated nonlinear data and investigation on the limit in practical use.(2) Research of descriptive statistics and statistical inference on multivariate analysis, and the understanding of their discrepancy.(3) Development of optimization theories in mathematical programming and model construction for applying the results to practical problems.(4) Investigation on asymptotic theory, large deviation theory, model selection in time series analysis and their application.(5) Investigation on the theories and methodologies of sample sizes in sequential analysis required to carry out efficient statistical inference.(6) Investigation on probability distributions and sampling distributions concerning various statistical models.(7) Investigation on combinatorial mathematics, integral conditions and optimization in statistical model construction and inference.(8) Development of the theories on computer-intensive statistical methods and construction of useful statistical software.(9) Development of statistical asymptotic theory and construction of the computer-intensive algorithms.(10) Investigation on statistical inference concerning multivariate model, stochastic process model, time siries model and Baysian model.(11) Construction of good estimators and joint confidence intervals, and investigation on their properties.