On Sequential Comparisons of Means of First-Order Autoregressive Models.
On sequential minimax estimation for the exponential class of processes
On sequential plans for the exponential class of processes
On some minimax sequential decision problems with partial observability
On the approximation of some optimal sequential plan
On the Asymptotic Behaviour of Linear Learning Processes with Partial Forgetting.
On the convergence of moments in the almost sure central limit theorem for stochastic approximation algorithms
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 convergence of the dynamic stochastic approximation method for stochastic non-linear multidimensional dynamic systems
On the dynamic stochastic approximation
On the evaluation of properties of the sequential probability ratio test for statistically dependent observations
On the inequality of Cramér-Rao type in sequential estimation theory
On the optimal continuous experimental design problem
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 Optimality of Differentiated SPR Tests of Composite Hypotheses.
On the optimum sequential test of two hypotheses for statistically dependent observations
On the Recursive Estimation of the Location and of the Size of the Mode of a Probability Density
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...
On the stability of interacting processes with applications to filtering and genetic algorithms
On the Two Armed Bandit with one Probability Known.
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...