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On sequential and fixed designs for estimation with comparisons and applications.

Mekki Terbeche, Broderick O. Oluyede, Ahmed Barbour (2005)

SORT

A fully sequential approach to the estimation of the difference of two population means for distributions belonging to the exponential family of distributions is adopted and compared with the best fixed design. Results on the lower bound for the Bayes risk due to estimation and expected costs are presented and shown to be of first order efficiency. Applications involving the Poisson and exponential distributions with gamma priors as well as the Bernouilli distribution with beta priors are given....

On the convergence of moments in the almost sure central limit theorem for stochastic approximation algorithms

Peggy Cénac (2013)

ESAIM: Probability and Statistics

We study the almost sure asymptotic behaviour of stochastic approximation algorithms for the search of zero of a real function. The quadratic strong law of large numbers is extended to the powers greater than one. In other words, the convergence of moments in the almost sure central limit theorem (ASCLT) is established. As a by-product of this convergence, one gets another proof of ASCLT for stochastic approximation algorithms. The convergence result is applied to several examples as estimation...

On the optimal continuous experimental design problem

Christos P. Kitsos (2011)

Discussiones Mathematicae Probability and Statistics

The target of this paper is to provide a compact review of the Optimal Experimental Design, the continuous case. Therefore we are referring to the general nonlinear problem in comparison to the linear one.

On the Recursive Estimation of the Location and of the Size of the Mode of a Probability Density

Djeddour, Khédidja, Mokkadem, Abdelkader, Pelletier, Mariane (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 62G07, 62L20.Tsybakov [31] introduced the method of stochastic approximation to construct a recursive estimator of the location q of the mode of a probability density. The aim of this paper is to provide a companion algorithm to Tsybakov's algorithm, which allows to simultaneously recursively approximate the size m of the mode. We provide a precise study of the joint weak convergence rate of both estimators. Moreover, we introduce the averaging principle...

Optimal sequential multiple hypothesis testing in presence of control variables

Andrey Novikov (2009)

Kybernetika

Suppose that at any stage of a statistical experiment a control variable X that affects the distribution of the observed data Y at this stage can be used. The distribution of Y depends on some unknown parameter θ , and we consider the problem of testing multiple hypotheses H 1 : θ = θ 1 , H 2 : θ = θ 2 , ... , H k : θ = θ k allowing the data to be controlled by X , in the following sequential context. The experiment starts with assigning a value X 1 to the control variable and observing Y 1 as a response. After some analysis, another value X 2 for...

Optimal sequential multiple hypothesis tests

Andrey Novikov (2009)

Kybernetika

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.

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