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Scientific learning is seen as an iterative process employing Criticism and Estimation. Sampling theory use of predictive distributions for model criticism is examined and also the implications for significance tests and the theory of precise measurement. Normal theory examples and ridge estimates are considered. Predictive checking functions for transformation, serial correlation, and bad values are reviewed as is their relation with Bayesian options. Robustness is seen from a Bayesian view point...
An asymptotic formula for the difference of the -estimates of the regression coefficients of the non-linear model for all observations and for observations is presented under conditions covering the twice absolutely continuous -functions. Then the implications for the -estimation of the regression model are discussed.
This paper deals with four types of point estimators based on minimization of information-theoretic divergences between hypothetical and empirical distributions. These were introduced (i) by Liese and Vajda [9] and independently Broniatowski and Keziou [3], called here power superdivergence estimators, (ii) by Broniatowski and Keziou [4], called here power subdivergence estimators, (iii) by Basu et al. [2], called here power pseudodistance estimators, and (iv) by Vajda [18] called here Rényi pseudodistance...
Two concepts of optimality corresponding to Bayesian robust analysis are considered: conditional Γ-minimaxity and stability. Conditions for coincidence of optimal decisions of both kinds are stated.
The problem of selecting a subset of polulations containing the population with the largest location parameter is considered. As a generalization of selection rules based on sample means and on sample medians, a rule based on -estimates of location is proposed. This rule is strongly monotone and minimax, the risk being the expected subset size, provided the underlying density has monotone likelihood ratio. The problem of fulfilling the -condition is solved explicitly only asymptotically, under...
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