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• W1844105024 abstract "This thesis is a study of several statistical modeling problems by stochastic complexity.At first, an index of predictive power, using the concept of complexity or minimum description length, is proposed as a criterion to select the principal components of a random vector distributed in a parametric family.Then, we consider the problem of selecting a model with the best predictive ability in a class of generalized linear models. A predictive least quasi-deviance criterion is proposed to measure the predictive ability of a model. Some results concerning the consistency of this criterion are given. The method is also modified for finite sample applications.Thirdly a density estimation based complexity decision rule is proposed, which uses the quality of these estimators to estimate the corresponding unknown element of the true probability density. The resulting complexity density decision procedures shown to be admissible, to achieve the minimum expected risk, and to form a minimal complete class.Fourthly a generalized histogram density estimator with unequal-width subintervals is used to find both optimal and predictive optimal description of a sample. Both optimal descriptions are expressed in terms of the stochastic complexity. Uniform, almost sure asymptotic expressions for both descriptions are given.Finally, as an application of the stochastic complexity for optimal data description, a new test procedure for hypotheses of homogeneity is proposed. Some examples and simulation studies are further given to illustrate this test procedure." @default.
• W1844105024 created "2016-06-24" @default.
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• W1844105024 date "1994-01-01" @default.
• W1844105024 modified "2023-10-05" @default.
• W1844105024 title "Statistical modeling by stochastic complexity" @default.
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