摘要:

We are dealing with the problems of estimating the mean of a negative binomial distribution. We propose various types of two stage sampling techniques for controlling the coefficient of variation or the construction of confidence intervals of prescribed accuracy. Asymptotic properties are derived, and the small sample performances are studied and contrasted with those of the purely sequential procedures of Willson and Folks (1983). In many situations, our new two stage procedures perform better.

ISSN:0747-4946    

DOI:10.1080/07474948508836069

出版商:Marcel Dekker, Inc.    

年代:1985

数据来源: Taylor

摘要:

A tail area influence function is introduced and, for tests Tndetermined as solutions ofsmall sample asymptotics are used to compute this influence function. Its relationship to other influence functions for testing is examined and it is shown to be a finite sample refinement of the level and power influence function. Approximations for the maximum level and minimum power for a gross error model are computed.

ISSN:0747-4946    

DOI:10.1080/07474948508836070

出版商:Marcel Dekker, Inc.    

年代:1985

数据来源: Taylor

摘要:

We consider estimation of a normal mean based on a sample of independent identically distributed observations from a normal population with unknown variance. A two stage procedure involves first taking an initial sample, on the basis of that sample deciding on the size of a second sample, and then estimating the mean based on the total sample. The loss is a linear combination of mean squared error and number of observations taken. We restrict attention to procedures which are shift invariant. We show that a complete class of procedures consists of those which choose the second sample size monotonically in the initial sample variance, obtain a class of natural Generalized Bayes procedures and an asymptotically minimax procedure among procedures with given initial sample size, and show that this latter procedure is admissible among the full class of equivariant procedures.

ISSN:0747-4946    

DOI:10.1080/07474948508836071

出版商:Marcel Dekker, Inc.    

年代:1985

数据来源: Taylor

摘要:

Conditions are given for weak convergence through random indices of a general stochastic approximation process which includes the Robbins-Monro and Kiefer-Wolfowitz processes. For a particular index, a sequential fixed-width bounded length confidence interval for the parameter being estimated is established. As an example, an optimal recursive estimator and confidence interval for the mode of a distribution function is constructed.

ISSN:0747-4946    

DOI:10.1080/07474948508836072

出版商:Marcel Dekker, Inc.    

年代:1985

数据来源: Taylor

摘要:

This paper considers a general stopping time based on U-statistics. The purpose is todevelop a general setting that will apply to many situations where the family ofdistributions from which we sample, is known apart from some unknown parameters.

ISSN:0747-4946    

DOI:10.1080/07474948508836073

出版商:Marcel Dekker, Inc.    

年代:1985

数据来源: Taylor

摘要:

Consider a population π composed of speciesin propotions p1,....pkrespectively. The population is searched by selecting a group of m randomly chosen members at a time.Let dm(n) denote the number of distinct species discovered in n selections.At stage n a reward offeris available to us where c > 0 is a fixed cost associated with each selection and h is a known, nondecreasing function defined over the set of positive integers. We wish to determine the time at which it is optimal to conclude the search. Some optimal and adaptive strategies are proposed.

ISSN:0747-4946    

DOI:10.1080/07474948508836074

出版商:Marcel Dekker, Inc.    

年代:1985

数据来源: Taylor

ISSN:0747-4946    

DOI:10.1080/07474948508836068

出版商:Marcel Dekker, Inc.    

年代:1985

数据来源: Taylor