A Self Critical Approach to Data Analysis and Model Building.
Final rept. 9 Jul 81-15 Jun 86,
RENSSELAER POLYTECHNIC INST TROY NY
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This report introduces a variety of new methods related to model construction, evolution. The most frequently encountered in practice specific cases are treated in substantial detail. e.g., experimental design layouts, regression, proportional hazards models, etc. The ultimate development is a generalization of the standard likelihood procedures for complete, censored, and binary data. This development includes estimation procedures, a test of hypothesis procedures asymptotic, and an objective test of adequacy for specific models. These objective tests require the development of special tables, some of which are given in this report. A close connection of the generalized likelihood with Fourier methods had been observed and exploited to arrive at the formal definition of the generalized likelihood. A number of results of independent interests are obtained via, and for Fourier concepts. The idea of a sensitivity analysis of a model is paramount throughout if the process of extraction of information from data vis-a-vis a tentative model is changed slightly, then the summarization or specification of this model should also change only slightly. Because our methods feed the estimation process back through the tentative model, the generalized likelihood procedures have been termed self-or model critical. Author
- Statistics and Probability