On the admissibility of tests for extended hypotheses of fit
On the convergence with probability one for a sequence of empirical Bayes estimators
On the experience utilization in statistical decisions
On the foundations of statistics and decision theory.
An elementary axiomatic foundation for decision theory is presented at a general enough level to cover standard applications of Bayesian methods. The intuitive meaning of both axioms and results is stressed. It is argued that statistical inference is a particular decision problem to which the axiomatic argument fully applies.
On the maximum probability criteria concerning the sequencial decision-making problem.
On the Natural Selection Rule in General Linear Models.
On the Optimality of Differentiated SPR Tests of Composite Hypotheses.
On the optimum sequential test of two hypotheses for statistically dependent observations
On the reducibility of a set of statistical hypotheses
On the use of the art of conjecture in juridical matters: what about (political) economics? (De usu artis conjectandi in jure: quid de oeconomia (politica)?)
On various criteria of optimality in probabilistic decision-making
Optimal alternative robustness in Bayesian Decision Theory.
In Martin et al (2003), we suggested an approach to general robustness studies in Bayesian Decision Theory and Inference, based on ε-contamination neighborhoods. In this note, we generalise the results considering neighborhoods based on norms, specifically, the supremum norm for utilities and the total variation norm for probability distributions. We provide tools to detect changes in preferences between alternatives under perturbations of the prior and/or the utility and the most sensitive direction....
Optimal choice of a statistical model: a discussion of the Akaike and classical approaches
Optimal decision rules
Optimal Regression Designs for Prediction when Prior Knowledge is Available.
Optimal sequential multiple hypothesis testing in presence of control variables
Suppose that at any stage of a statistical experiment a control variable that affects the distribution of the observed data at this stage can be used. The distribution of depends on some unknown parameter , and we consider the problem of testing multiple hypotheses , , allowing the data to be controlled by , in the following sequential context. The experiment starts with assigning a value to the control variable and observing as a response. After some analysis, another value for...
Optimal sequential multiple hypothesis tests
This work deals with a general problem of testing multiple hypotheses about the distribution of a discrete-time stochastic process. Both the Bayesian and the conditional settings are considered. The structure of optimal sequential tests is characterized.
Optimal sequential procedures with Bayes decision rules
In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does not exceed some given bound. We characterize the form of optimal sequential stopping rules in this problem. In particular, we have a characterization of the form of optimal sequential decision procedures when the Bayesian risk includes both the loss due to incorrect...
Optimal streams of premiums in multiperiod credibility models
Optimal arrangement of a stream of insurance premiums for a multiperiod insurance policy is considered. In order to satisfy solvency requirements we assume that a weak Axiom of Solvency is satisfied. Then two optimization problems are solved: finding a stream of net premiums that approximates optimally 1) future claims, or 2) "anticipating premiums". It is shown that the resulting optimal streams of premiums enable differentiating between policyholders much more quickly than one-period credibility...
Oracle inequalities and nonparametric function estimation.