Showing papers on "Sequential probability ratio test published in 1982"

Likelihood ration test, Wald test and Kuhn-Tucker test in linear-models with inequality constraints on the regression parameters Likelihood Ratio Test, Wald Test and Kuhn-Tucker Test in Linear Models with Inequality Constraints on the Regression Parameters

Abstract: This paper considers the problem of testing statistical hypotheses in linear regression models with inequality constraints on the regression coefficients. The Kuhn-Tucker multiplier test statistic is defined and its relationships with the likelihood ratio test and the Wald test are examined. It is shown, in particular, that these relationships are the same as in the equality constrained case. It is emphasized, however, that their common asymptotic distribution is a mixture of chi-square distributions under the null hypothesis.

The Likelihood Ratio, Wald, and Lagrange Multiplier Tests: An Expository Note

Abstract: By means of simple diagrams this note gives an intuitive account of the likelihood ratio, the Lagrange multiplier, and Wald test procedures. It is also demonstrated that if the log-likelihood function is quadratic then the three test statistics are numerically identical and have χ2 distributions for all sample sizes under the null hypothesis.

Asymptotic efficiencies of truncated sequential tests

Abstract: Truncation of a sequential test with constant boundaries is considered for the problem of testing a location hypothesis: f(x- \theta_{0}) versus f(x- \theta_{1}) . A test design procedure is developed by using bounds for the error probabilities under the hypothesis and alternative. By viewing the truncated sequential test as a mixture of a sequential probability ratio test and a fixed sample size test, its boundaries and truncation point can be obtained once the degree of mixture is specified. Asymptotically correct approximations for the operating characteristic function and the average sample number function of the resulting test are derived. Numerical results show that an appropriately designed truncated sequential test performs favorably as compared to both the fixed sample size test and the sequential probability ratio test with the same error probabilities. The average sample number function of the truncated test is uniformly smaller than that of the fixed sample size test, and the truncated test maintains average sample sizes under the hypothesis and the alternative that are close to those optimum values achieved by Wald's sequential probability ratio test. Moreover, the truncated test is more favorable than the sequential probability ratio test in the sense that is has smaller average sample size when the actual location parameter is between \theta_{0} and \theta_{1} . This behavior becomes more pronounced as the error probabilities become smaller, implying that the truncated sequential test becomes more favorable as the error probabilities become smaller.

Sequential statistical procedures for processes of the exponential class with independent increments

Abstract: In this survey paper sequential statistical procedures for the exponential class of processes with independent increments are considered. After the definition of the exponential class a characterization in terms of the LEVY-CHXNTCBXN.representation is given. Then, sequential estimation problems* and sequential testing of hypotheses with respect to the underlying parameter are studied. Finally, some possible extensions of the considered notions and methods to other classes of processes are indicated.

A sequential likelihood ratio test for general hypotheses

Abstract: In statistical inference it is often desired to test a specified funcrion of unkown parameters form an underlying distribution. Sequential procedures utilize information from the already collected observations and allow for a possible eariy termination of experimentation with a concurrent savings in time and cost. In the present work a suitable maximum-likelihood based sequential testing procedure for functions of unknown parameters is developed for independent and identically distributed observations of an underlying distribution of known form. The theoretical Operating Characteristic (OC) and Average Sample Number (ASN) functions are derived for local alternatives by approximating the distribution of the test statistic with linear combinations of the standard Wiener process, Simlriation studies were utilized to investigate the goodness of the asymptotic results in finite samples.

On a direct method of analysis and synthesis of the SPRT

Abstract: The behavior of the sequential probability ratio test (SPRT) can be described using four performance measures, i.e., the probabilities of both types of error \alpha_{0}, \alpha_{1} , and the average test lengths (or sample sizes) E_{0}, E_{1} for the given decision problem. Whereas Bayes optimality of the SPRT is well-known from the work of Wald and Wolfowitz, there is no method to evaluate the performance measures except for Wald's approximations. We present a method to evaluate the performance measures given the thresholds of the SPRT.

Properties of a distribution-free two-stage two-sample median test

Abstract: In this paper we consider a class of distribution-free two-stage two-sample median tests. These procedures are based on a fixed size sample from one population, while the observations from the second population are collected in a truncated sequential fashion. Necessary tables are provided enabling us to select a particular member from the class such that arbitrarily preset power levels are approximately obtained. We also present asymptotic expressions and tables for the expected number of observations from the second population. Finally, comparisons between the asymptotic version of this two-stage median test and the binomial sequential probability ratio test due to Wald (1947) are discussed.

Sequential procedures for a class of distributions related to the uniform

Abstract: The main purpose of this paper is to examine some sequential inference procedures, mainly in the one-sided hypothesis testing situation, for the parameter of a class of distributions related to the Uniform distribution on (0, θ). The procedures are all based on the sequence of maxima of independent and identically distributed random variables and, for the case of a single (upper) boundary, procedures which are optimal in the sense of minimizing the average sample size are discussed. The impossibility of using two boundaries is demonstrated, thus leaving the best procedure with one boundary as the optimal procedure. The novelty of this procedure is that it uniformly minimizes the average sample size.

Use of a sequential probability ratio test to assess sib content in brassica oleracea

Abstract: SUMMARY Seed lots of F1 hybrids of Brassica oleracea are unmarketable if they contain too many sibs. The modified sequential probability ratio test (SPRT) proposed by Whitehead (1981) can be used to determine whether a hybrid seed lot meets specified quality standards for sib content and to estimate the actual proportion of sibs. It is more economical in testing than a single-sample procedure of equal accuracy and is particularly suited for use with electrophoretic methods of sib recognition. A computer program has been written to produce control charts, for a range of test standards, for direct plotting of results.