Minimax sequential estimation for the multinomial and gamma processes

The Asymptotic Minimax Risk for the Estimation of Constrained Binomial and Multinomial Probabilities

In this paper we present a direct and simple approach to obtain bounds on the asymptotic minimax risk for the estimation of constrained binomial and multinomial proportions. Quadratic, normalized quadratic and entropy loss are considered and it is demonstrated that in all cases linear estimators are asymptotically minimax optimal. For the quadratic loss function the asymptotic minimax risk does...

the search for the self in becketts theatre: waiting for godot and endgame

this thesis is based upon the works of samuel beckett. one of the greatest writers of contemporary literature. here, i have tried to focus on one of the main themes in becketts works: the search for the real "me" or the real self, which is not only a problem to be solved for beckett man but also for each of us. i have tried to show becketts techniques in approaching this unattainable goal, base...

Parameter Estimation for the Dirichlet-Multinomial Distribution

In the 1998 paper entitled Large Cluster Results for Two Parametric Multinomial Extra Variation Models, Nagaraj K. Neerchal and Jorge G. Morel developed an approximation to the Fisher information matrix used in the Fisher Scoring algorithm for finding the maximum likelihood estimates of the parameters of the Dirichlet-multinomial distribution. They performed simulation studies comparing the res...

Sequential Minimax Search for a Maximum

The problem formulated below was motivated by that of determining an interval containing the point at which a unimodal function on the unit interval possesses a maximum, without postulating regularity conditions involving continuity, derivatives, etc. Our solution is to give, for every e > 0 and every specified number N of values of the argument at which the function may be observed, a procedur...

Minimax lower bounds for estimation