On a Stopping Rule for a Class of Sequential Decision Problems.
On an asymptotic optimality property of play-the-winner and vector-at-a-time sampling.
Simon and Weiss (1975) consider the formulation of the clinical trial as a selection procedure (Bechhofer, Kiefer and Sobel, 1968). The object of the trial is to choose the better treatment with probability ≥ P*, where P* is assigned, when the difference in success probabilities is ≥ Δ*, Δ* also being assigned. They consider a family of single step allocation methods for the reduction of the number of patients given the poorer treatment. Using numerical results, Simon and Weiss conclude that if...
On optimal stopping of inhomogeneous standard Markov processes.
On randomized stopping times.
In this note we give a proof of the fact that the extremal elements of the set of randomized stopping times are exactly the stopping times.
On sequential plans for the exponential class of processes
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 stopping of a random length sequence of maxima over a random barrier
Optimal stopping of a sequence of maxima over an unobservable sequence of maxima
Optimum stopping rules on the sequence of statistically dependent vectors
Parametrization and geometric analysis of coordination controllers for multi-agent systems
In this paper, we address distributed control structures for multi-agent systems with linear controlled agent dynamics. We consider the parametrization and related geometric structures of the coordination controllers for multi-agent systems with fixed topologies. Necessary and sufficient conditions to characterize stabilizing consensus controllers are obtained. Then we consider the consensus for the multi-agent systems with switching interaction topologies based on control parametrization.
Remarks on Sequential Estimation of a Linear Function of Two Means: The Normal Case.
Risk-Efficient Nonparametric Sequential Estimators.
Secretary Problems with Inspection Costs as a Game.
Sequential estimation of powers of a scale parameter from delayed observations
The problem of sequentially estimating powers of a scale parameter in a scale family and in a location-scale family is considered in the case when the observations become available at random times. Certain classes of sequential estimation procedures are derived under a scale invariant loss function and with the observation cost determined by a convex function of the stopping time and the number of observations up to that time.
Sequential risk-efficient estimation of the parameter in the uniform density.
Sequential statistical structures
Some Best Possible Results for a Discounted One Armed Bandit.
Stability estimating in optimal sequential hypotheses testing
We study the stability of the classical optimal sequential probability ratio test based on independent identically distributed observations when testing two simple hypotheses about their common density : versus . As a functional to be minimized, it is used a weighted sum of the average (under ) sample number and the two types error probabilities. We prove that the problem is reduced to stopping time optimization for a ratio process generated by with the density . For being the corresponding...