摘要:

A class of robuet estimates of location uses the Robbins-Monro stochastic approximation algorithm as a basis. These estimates, called SA-estimates, have been proposed by Martin (1972), who established an asymptotic min-max result like that of P. Huber (1964) for M-estimates. Here we study in detail the small sample behavior of robust SA-estimates for location at sample sizes N = 10, 20, 40 using Monte Carlo swindle techniques. Results are presented for point estimate efficiencies and for error rates and expected confidence interval lengths obtained by studentizing through use of the natural estimate of the asymptotic variance formula. Unlike M-estimates, SA-estimates are not invariant under permutations of the data order. Thus our study included one-step M-estimates and iterated- weighted least squares estimates. This was done not only for comparison purposes, but also because the latter are of interest in their own right. The results show that SA-estimate losses due to the lack of invariance under permutation of the data order are small, and that the performance of various SA-estimates compares favorably with that of M-estimates.

ISSN:0361-0918    

DOI:10.1080/03610918408812357

出版商:Marcel Dekker, Inc.    

年代:1984

数据来源: Taylor

摘要:

This article is concerned with modifications of both maximum likelihood and moment estimators for parameters of the three parameter inverse Gaussian distribution . Modifications presented here are essentially the same as those previously proposed by Cohen and Whitten (1980, 1981, 1982a, 1982b) in connection with the 1ognormal, gama and Weibull distributions . Computer programs have been prepared for the practical application of these estimators and an illustrative example is included. Results of a simulation study provide insight into the sampling behavior of the new estimators and include comparisons with the traditional moment and maximum likelihood estimators with respect to bias and standard deviations of estimates. For some combinations of parameter values, some of the modified estimators considered here enjoy advantages over both moment and maximum likelihood estimators with respect to bias, variance, and/or ease of computation.

ISSN:0361-0918    

DOI:10.1080/03610918408812358

出版商:Marcel Dekker, Inc.    

年代:1984

数据来源: Taylor

摘要:

Prior information regarding the interrelation of two Bernoulli processes may justify a clinical trial designed to corroborate this information. Antelman (1973) has studied the Dirichlet-beta which permits the expression of the prior knowledge of such interrelation. However, use of this prior distribution leads to complicated and intractable analyses. Alternately, such prior information regarding the interrelation of the processes may be adequately summarized by a simple Dirichlet distribution. Procedures for testing hypotheses regarding a priori interrelations of the success probabilities of the processes are given. Exact expressions for the posterior probabi1ities of these hypotheses are shown to be approximately equal to weighted p-values or 1ikelihood ratios.

ISSN:0361-0918    

DOI:10.1080/03610918408812359

出版商:Marcel Dekker, Inc.    

年代:1984

数据来源: Taylor

摘要:

Additive and multiplicative heteroscedastic error models are considered, and the relative efficiency of a number of Bayesian and sampling theory estimators, including some pre-test estimators,is investigated. The relative performance of the various estimators seems to depend more on sample size and the severity of the heteroscedasticity than it does on the underlying nature of the heteroscedasticity. In general the Bayesian estimators outperform the sampling theory estimators, and we make some useful recommendations concerning estimator choice.

ISSN:0361-0918    

DOI:10.1080/03610918408812360

出版商:Marcel Dekker, Inc.    

年代:1984

数据来源: Taylor

摘要:

A set of independent observations is assumed to come from one or more normal populations having the same unknown variance and different unknown means. Ignorance priors are associated with these parameters. The number of populations is also unknown as is the number of observations from each, but priors are chosen for these quantities which make it very likely that one population is dominant. Observations from the rest are considered outliers. Using these priors in conjunction with Akaike's predictive likelihood, which is derived for the class of models considered, one can obtain a quasi-Bayesian posterior probability for each possible model. A “robust” estimate of the mean value of the dominant population and “corrected” values for the outliers can be calculated from the posterior probabilities, once the outliers have been designated. Darwin's data and Herndon's data are analyzed to illustrate the procedure.

ISSN:0361-0918    

DOI:10.1080/03610918408812361

出版商:Marcel Dekker, Inc.    

年代:1984

数据来源: Taylor

摘要:

Recently, a lot of attention has been brought to constrained estimation theory in multidimensional scaling models. So far, only equality constraints have been thoroughly studied. In this paper, the optimization theory is extended to general multidi-mensional scaling models with both inequality and equality constraints. A Newton-Raphson based algorithm is developed to produce the constrained least squares estimate. To illustrate the theory, some classical color data are reanalyzed in the context of the linear Euclidean distance model.

ISSN:0361-0918    

DOI:10.1080/03610918408812362

出版商:Marcel Dekker, Inc.    

年代:1984

数据来源: Taylor

ISSN:0361-0918    

DOI:10.1080/03610918408812356

出版商:Marcel Dekker, Inc.    

年代:1984

数据来源: Taylor