摘要:

AbstractFor a moderate or large number of regression coefficients, shrinkage estimates towards an overall mean are obtained by Bayes and empirical Bayes methods. For a special case, the Bayes and empirical Bayes shrinking weights are shown to be asymptotically equivalent as the amount of shrinkage goes to zero. Based on comparisons between Bayes and empirical Bayes solutions, a modification of the empirical Bayes shrinking weights designed to guard against unreasonable overshrinking is suggested. A numerical example is given.

ISSN:0319-5724    

DOI:10.2307/3315184

出版商:Wiley‐Blackwell    

年代:1986

数据来源: WILEY

摘要:

AbstractA set ofppopulations is subjected to a first sampling. From this, it is required to select one of the populations so that the mean of a future sample is maximized. Extensions to this problem are discussed and solved by the use of predictive densities. These results are finally adapted to populations with covariate structure under systems of balanced sampling. Applications to quantitative genetics are indicated.

ISSN:0319-5724    

DOI:10.2307/3315185

出版商:Wiley‐Blackwell    

年代:1986

数据来源: WILEY

摘要:

AbstractLet a groupGact on the sample space. This paper gives another proof of a theorem of Stein relating a group invariant family of posterior Bayesian probability regions to classical confidence regions when an appropriate prior is used. The example of the central multivariate normal distribution is discussed.

ISSN:0319-5724    

DOI:10.2307/3315186

出版商:Wiley‐Blackwell    

年代:1986

数据来源: WILEY

摘要:

AbstractPartial specification of a prior distribution can be appealing to an analyst, but there is no conventional way to update a partial prior. In this paper, we show how a framework for Bayesian updating with data can be based on the Dirichlet(a) process. Within this framework, partial information predictors generalize standard minimax predictors and have interesting multiple‐point shrinkage properties. Approximations to partial‐information estimators for squared error loss are defined straightforwardly, and an estimate of the mean shrinks the sample mean. The proposed updating of the partial prior is a consequence of four natural requirements when the Dirichlet parameter a is continuous. Namely, the updated partial posterior should be calculable from knowledge of only the data and partial prior, it should be faithful to the full posterior distribution, it should assign positive probability to every observed event {X,}, and it should not assign probability to unobserved events not included in the partial prior specificat

ISSN:0319-5724    

DOI:10.2307/3315187

出版商:Wiley‐Blackwell    

年代:1986

数据来源: WILEY

摘要:

AbstractA Bayesian nonparametric estimate of the survival distribution is derived under a particular sampling scheme for grouped data that includes the possibility of censoring. The estimate uses the prior information to smooth the data, giving an estimate which is continuous. As special cases survival estimates for life tables are obtained and the estimate of Susarla and Van Ryzin (1976) is derived. As the weight of the prior information tends to zero, the Bayesian estimate reduces to a continuous version of the nonparametric maximum‐likelihood estimate. An empirical Bayes modification of the procedure is illustrated on a data set from Cutler and Ederer (1958

ISSN:0319-5724    

DOI:10.2307/3315188

出版商:Wiley‐Blackwell    

年代:1986

数据来源: WILEY

摘要:

AbstractInvariant confidence regions with smallest expected normalized volume are derived for a matrix of means of interest in the GMANOVA model, assuming only that the distribution of the matrix of residuals is left orthogonally invariant. Two invariance groups are considered, the usual full group and an amenable subgroup. A particular choice of the normalizing term leads to conditionally optimal confidence regions. Numerical results are given comparing the conditionally optimal fully invariant confidence region, which corresponds to the likelihood‐ratio test, with a conditionally minimax confidence regio

ISSN:0319-5724    

DOI:10.2307/3315189

出版商:Wiley‐Blackwell    

年代:1986

数据来源: WILEY

摘要:

AbstractThe censoring principle is shown to imply a principle similar to the likelihood principle. Further, it is demonstrated that the censoring principle and a weak form of the conditionality principle jointly imply the likelihood principle.

ISSN:0319-5724    

DOI:10.2307/3315190

出版商:Wiley‐Blackwell    

年代:1986

数据来源: WILEY

摘要:

AbstractThe characteristic function of the multivariate Studentt‐distribution is obtained, and it is shown that this characteristic function has the pedogogical virtue of reducing the multivariate problem to the analogous univariate problem. Applications of the characteristic function are discusse

ISSN:0319-5724    

DOI:10.2307/3315191

出版商:Wiley‐Blackwell    

年代:1986

数据来源: WILEY

摘要:

AbstractOptimality properties of multiway block designs are deduced from the general results of J. Kiefer's approximate‐design theory. In the model with additive effects these optimality properties solely depend on the two‐dimensional marginals of the designs. Uniform designs, and designs whose two‐dimensional marginals are products of the one‐dimensional marginals, are shown to be optimal. Approximate Youden designs are introduced for the case when the support sets of the two‐dimensional marginals are prescribed in advance. They are optimal in a relatively small class of competing des

ISSN:0319-5724    

DOI:10.2307/3315192

出版商:Wiley‐Blackwell    

年代:1986

数据来源: WILEY

摘要:

AbstractThe binomial, Poisson, logarithmic, negative binomial, and extended negative binomial distributions are characterized in the class of power‐series distributions (1) through a differential equation based on the ratio of two successive derivatives of the series function, (2) through the ratio of two probabilities associated with two successive values in the range of the random variable, and (3) through the ratio of two consecutive factorial moments. The ratios referred to in (2) and (3) above can be utilized to discriminate between the five power‐series distributions mentioned at the beginn

ISSN:0319-5724    

DOI:10.2307/3315193

出版商:Wiley‐Blackwell    

年代:1986

数据来源: WILEY