摘要:

We present designs that perform well for several objectives simultaneously. Three different approaches are discussed: to augment a given design in an optimal way, to evaluate a mixture of the various criteria, and to optimize one objective subject to achieving a prescribed efficiency level for the others. Our sample designs are for the situation of discriminating between a second- and third-degree polynomial fit, under theD-criterion and geometric mixtures ofD-criteria.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476317

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

A class of independent linear models is considered, where the variances of the different models are unequal but they have a common vector parameterθoccurring in their mean vectors. For testing the hypothesisH0:θ= 0, some exact test procedures are derived that combine the information from all the models. The procedures are extensions of the test suggested by Cohen and Sackrowitz for recovering interblock information in balanced incomplete block designs. Simulation results on the power of the new tests and some standard tests are reported in the context of (1) testing the hypothesis concerning the common mean of two univariate normal populations and (2) recovering interblock information in a block design that is not a balanced incomplete block design. The numerical results indicate that the new tests have excellent performance in terms of power compared to some standard tests.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476318

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Using a general method for obtaining confidence intervals from samples from discrete distributions, this article introduces a new confidence interval method for estimating the difference of two binomial probabilities and compares it to three other confidence interval methods, one of which is the usual method with no continuity correction. Each of the other two confidence interval methods uses its own continuity correction; one combines it with an estimate of the standard error that is slightly different from that commonly used. Some values of the “exact” confidence interval limits are also derived. The four confidence interval methods, each of which is based on the normal approximation and can be carried out easily on a hand calculator, are compared in terms of their precision, the agreement of their coverage probabilities with nominal confidence level values, and the smallness of their sample sizes before the normal approximation can be considered appropriate. Coverage probabilities and measures of precision are computed exactly rather than estimated by simulation. On the basis of these comparisons, the new confidence interval method is recommended.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476319

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

We consider the problem of estimating probabilities for the different numbers in a lottery when the winning numbers are selected sequentially without replacement. Numerical methods are developed to compute maximum likelihood estimates of the probabilities and their variance-covariance matrix based on observed outcomes. The generalized likelihood ratio statistic –2 ln(λ) for testing equiprobable numbers is also given. The methods are applied to a data set from the Lotto America lottery. The properties of the procedure are studied by simulation.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476320

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

A vast literature in statistics, biometrics, and econometrics is concerned with the analysis of binary and polychotomous response data. The classical approach fits a categorical response regression model using maximum likelihood, and inferences about the model are based on the associated asymptotic theory. The accuracy of classical confidence statements is questionable for small sample sizes. In this article, exact Bayesian methods for modeling categorical response data are developed using the idea of data augmentation. The general approach can be summarized as follows. The probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data. Values of the latent data can be simulated from suitable truncated normal distributions. If the latent data are known, then the posterior distribution of the parameters can be computed using standard results for normal linear models. Draws from this posterior are used to sample new latent data, and the process is iterated with Gibbs sampling. This data augmentation approach provides a general framework for analyzing binary regression models. It leads to the same simplification achieved earlier for censored regression models. Under the proposed framework, the class of probit regression models can be enlarged by using mixtures of normal distributions to model the latent data. In this normal mixture class, one can investigate the sensitivity of the parameter estimates to the choice of “link function,” which relates the linear regression estimate to the fitted probabilities. In addition, this approach allows one to easily fit Bayesian hierarchical models. One specific model considered here reflects the belief that the vector of regression coefficients lies on a smaller dimension linear subspace. The methods can also be generalized to multinomial response models withJ> 2 categories. In the ordered multinomial model, theJcategories are ordered and a model is written linking the cumulative response probabilities with the linear regression structure. In the unordered multinomial model, the latent variables have a multivariate normal distribution with unknown variance-covariance matrix. For both multinomial models, the data augmentation method combined with Gibbs sampling is outlined. This approach is especially attractive for the multivariate probit model, where calculating the likelihood can be difficult.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476321

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

In standard saddlepoint approximations to the cumulative distribution function of a random variable, the normal distribution has appeared to play a special role. In this article we consider what happens when the normal “base” distribution is replaced by an arbitrary base distribution. Generalized versions of several standard formulas, are presented. The choice of a chi-squared base or an inverse Gaussian base is then considered in detail. The generalized approximations are compared in two examples: a linear combination of chi-squared variables and the first passage time distribution for a random walk. The former example considers approximations using the chi-squared base that are slightly more accurate than their normal-based counterparts. In the latter example, approximations based on the inverse Gaussian are considerably more accurate than their normal-based counterparts.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476322

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The number of successes out of the total number of trials is observed for each of a set ofNindependent binomial experiment's and the associated success probabilities are compared. Ranking procedures for comparing these success probabilities are constructed under circumstances where the number of trials for each of the experiments may differ by a large amount. A loss function is constructed that represents an appropriate measure of distance between a given ranking of the success probabilities and their true ranking. Bayes and empirical Bayes procedures based on this loss function are proposed and compared with “adapted ranking procedures” that arise through Bayes, empirical Bayes, or maximum likelihood estimation of the success probabilities. Bayes and empirical Bayes ranking procedures are shown to be transitive. Empirical Bayes ranking procedures are shown to arise from maximizing a function of the prior parameters that measures the amount of confidence enjoyed by various Bayes procedures. These results are applied to comparing the prevalence of toxoplasmosis for different small communities in El Salvador and comparing the batting averages of baseball players in the World Series.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476323

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Perspectives on Contemporary Statistics.David C. Hoaglin and David S. Moore (eds.). Washington: Mathematical Association of America, 1991. xiii + 192 pp. $20.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476324

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476325

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476329

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor