Notes on stochastic approximation methods
O stochastické aproximaci
On a class of discrete generation interacting particle systems.
On a Stochastic Approximation Procedure Based on Averaging.
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 Bather's stochastic approximation algorithm
On calculating the Laplace transform of a special quadratic functional of the Ornstein-Uhlenbeck velocity process
On computing the OC and ASN for some Markovian SPRT's
On domination and sufficiency in sequential analysis
On Estimating the Reliability After Sequentially Estimating the Mean: The Exponential Case.
On estimation of a covariance function of stationary errors in a nonlinear regression model.
On integer stochastic approximation
Let be observable, with experimental errors, at integer points only; unknown elsewhere. Iterative nonparametric procedures for finding the zero point of are called procedures of integer stochastic approximation. Three types of such procedures (Derman’s, Mukerjee’s and the authors’) are described and compared. A two-dimensional analogue of the third approach is proposed and investigated; its generalization to higher dimensions is conjectured.
On minimax sequential estimation of the mean value of a stationary Gaussian Markov process
On minimax sequential procedures for exponential families of stochastic processes
The problem of finding minimax sequential estimation procedures for stochastic processes is considered. It is assumed that in addition to the loss associated with the error of estimation a cost of observing the process is incurred. A class of minimax sequential procedures is derived explicitly for a one-parameter exponential family of stochastic processes. The minimax sequential procedures are presented in some special models, in particular, for estimating a parameter of exponential families of...
On multiple test procedures
On optimal stopping of inhomogeneous standard Markov processes.
On optimality of the LR tests in the sense of exact slopes. II. Application to individual distributions
On optimality of the LR tests in the sense of exact slopes. I. General case
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.