Sequential Tests Of Composite Hypotheses Research Articles

Nearly optimal sequential tests of composite hypotheses revisited

We revisit the problem of sequential testing composite hypotheses, considering multiple hypotheses and very general non-i.i.d. stochastic models. Two sequential tests are studied: the multihypothesis generalized sequential likelihood ratio test and the multihypothesis adaptive sequential likelihood ratio test with one-stage delayed estimators. While the latter loses information compared to the former, it has an advantage in designing thresholds to guarantee given upper bounds for probabilities of errors, which is practically impossible for the generalized likelihood ratio type tests. It is shown that both tests have asymptotic optimality properties minimizing the expected sample size or even more generally higher moments of the stopping time as probabilities of errors vanish. Two examples that illustrate the general theory are presented.

Nearly Optimal Sequential Tests of Composite Hypotheses Revisited

Nearly Optimal Sequential Tests of Composite Hypotheses Revisited

Importance Sampling for Generalized Likelihood Ratio Procedures in Sequential Analysis

This paper describes importance sampling techniques for Monte Carlo computation of the error probabilities and false alarm rates of sequential GLR (generalized likelihood ratio) tests and detection rules. It also discusses asymptotically optimal choice of the proposal distributions for importance sampling and gives numerical comparisons of the sequential GLR procedures with other sequential tests of composite hypotheses and detection rules in the literature.

Asymptotic approximations for error probabilities of sequential or fixed sample size tests in exponential families

Asymptotic approximations for the error probabilities of sequential tests of composite hypotheses in multiparameter exponential families are developed herein for a general class of test statistics, including generalized likelihood ratio statistics and other functions of the sufficient statistics. These results not only generalize previous approximations for Type I error probabilities of sequential generalized likelihood ratio tests, but also pro- vide a unified treatment of both sequential and fixed sample size tests and of Type I and Type II error probabilities. Geometric arguments involving integration over tubes play an important role in this unified theory.

Nearly Optimal Sequential Tests of Composite Hypotheses

A simple class of sequential tests is proposed for testing the one-sided composite hypotheses $H_0: \theta \leq \theta_0$ versus $H_1: \theta \geq \theta_1$ for the natural parameter $\theta$ of an exponential family of distributions under the 0-1 loss and cost $c$ per observation. Setting $\theta_1 = \theta_0$ in these tests also leads to simple sequential tests for the hypotheses $H: \theta \theta_0$ without assuming an indifference zone. Our analytic and numerical results show that these tests have nearly optimal frequentist properties and also provide approximate Bayes solutions with respect to a large class of priors. In addition, our method gives a unified approach to the testing problems of $H$ versus $K$ and also of $H_0$ versus $H_1$ and unifies the different asymptotic theories of Chernoff and Schwarz for these two problems.

Minimax sequential tests of composite hypotheses on the drift of a Wiener process

A Wiener process with unknown drift parameter μ is, beginning at O, observed continuously and one has to decide between the hypotheses μ≤0 and μ>0. For loss functions of the form sμr and linear cost functions one wants to determine a minimax sequential test. Generalizing the results of DeGroot (1960) a minimax test in the class of all symmetrical SPRT’s is given in an explicit form. On the other hand it is shown that this SPRT is, in general, no longer minimax in the class of all sequential tests.

Approximations to Bayesian Sequential Tests of Composite Hypotheses

Approximations to Bayesian Sequential Tests of Composite Hypotheses

Sequential Tests for Composite Hypotheses with Two Binomial Populations

Summary Sequential procedures for testing composite hypotheses about the parameters of two binomial distributions are developed. The testing of a null hypothesis against a onesided alternative is studied. It is shown that SPRT tests of simple hypotheses can be used for the composite situation with the desired error probabilities being preserved. Computer simulations indicate that when discrimination is based upon the difference in success probabilities, a procedure based on a likelihood ratio with nuisance parameters replaced by sequential maximum-likelihood estimates is shown to result in the smallest expected sample size.

Corrections and Amendments: `Sequential Tests of Composite Hypotheses'

Corrections and Amendments: `Sequential Tests of Composite Hypotheses'

Sequential Tests of Composite Hypotheses

Abstract A method is given for obtaining sequential tests of composite hypotheses for a certain class of distributions. Approximate properties of the tests are derived and the method illustrated.

Sequential Tests of Composite Hypotheses

Abstract A method is given for obtaining sequential tests of composite hypotheses for a certain class of distributions. Approximate properties of the tests are derived and the method illustrated.

Sequential Tests of Composite Hypotheses

Sequential Tests of Composite Hypotheses

Sequential tests of composite hypotheses

Sequential tests of composite hypotheses

On a property of the sequentialt-test

Abstract 1. Introduction. In one of his papers [1], and later in his book on sequential analysis [2], Wald introduced a general method for constructing sequential tests of composite hypotheses and applied the method to construct a sequential t-test. Since Wald devoted a considerable amount of space and mathematics on his t-test, it has been taken for granted that he proved certain optimum properties of the test. It is the purpose of this note to show that the test cannot possess one of the properties thought to hold for it.

Sequential tests for composite hypotheses

AbstractA method is given for obtaining sequential tests in the presence of nuisance parameters. It is assumed that a jointly sufficient set of estimators exists for the unknown parameters. A number of special tests are described and their properties discussed.