摘要:

AbstractA linear pivotal is introduced as a generalization of an estimate. The defining feature of a linear pivotal is that it generates a likelihood function in the same way as does a statistic. This allows the efficiency and sufficiency of the pivotal to be examined. The efficient reduction of data to a linear pivotal can often be achieved when it cannot be achieved using an estimate. Maximum‐likelihood estimation can be interpreted as a method of generating approximate sufficient linear pivotal

ISSN:0319-5724    

DOI:10.2307/3315411

出版商:Wiley‐Blackwell    

年代:1990

数据来源: WILEY

ISSN:0319-5724    

DOI:10.2307/3315412

出版商:Wiley‐Blackwell    

年代:1990

数据来源: WILEY

ISSN:0319-5724    

DOI:10.2307/3315413

出版商:Wiley‐Blackwell    

年代:1990

数据来源: WILEY

摘要:

AbstractAn increase in kurtosis is achieved through the location‐ and scale‐free movement of probability mass from the “shoulders” of a distribution into its centre and tails. We introduce a coherent structure of ordering and measures, requiring no symmetry assumption, that represent different formalizations of this movement. For this purpose spread functions and spread‐spread plots are defined. The orderings impose growth patterns on the spread‐spread plot of the distributions involved, and the weakest involve both a specific scale‐matching technique and placement of “shoulders”. The role of existing kurtosis orderings and measures in this general context is identified and examples dis

ISSN:0319-5724    

DOI:10.2307/3315414

出版商:Wiley‐Blackwell    

年代:1990

数据来源: WILEY

摘要:

AbstractShrinkage estimators are often obtained by adjusting the usual estimator towards a target subspace to which the true parameter might belong. However, meaningful reductions in risk below the usual estimator can typically be achieved in a very small part of the parameter space. In the multivariate‐normal mean estimation problem, E. George, in a series of papers, showed how multiple‐shrinkage estimators (data‐weighted averages of several different shrinkage estimators) can attain substantial risk reductions in a large part of the parameter space. This paper extends the multiple‐shrinkage results to the case of simultaneous estimation of the means of several one‐parameter exponential families. Our results are developed by using an identity similar to that of Haff and Johnson (1986). A computer simulation is reported to indicate the magnitude of reductions in risk. Our results are also applied to the problem of how to choose appropriate component variables to combine before a suitable shrinkage estimator is c

ISSN:0319-5724    

DOI:10.2307/3315415

出版商:Wiley‐Blackwell    

年代:1990

数据来源: WILEY

摘要:

AbstractWe consider the problem of minimax‐variance, robust estimation of a location parameter, through the use ofL‐ andR‐estimators. We derive an easily checked necessary condition forL‐estimation to be minimax, and a related sufficient condition forR‐estimation to be minimax. Those cases in the literature in whichL‐estimation is known not to be minimax, and those in whichR‐estimation is minimax, are derived as consequences of these conditions. New classes of examples are given in each case. As well, we answer a question of Scholz (1974), who showed essentially that the asymptotic variance of anR‐estimator never exceeds that of anL‐estimator, if both are efficient at the same strongly unimodal distribution. Scholz raised the question of whether or not the assumption of strong unimodality could be dropped. We answer this question in the negative, theoretically and by examples. In the examples, the minimax property fails both forL‐estimation and forR‐estimation, but the variance of theL‐estimator, as the distribution of the observation varies over the given neighbourhood, remains unbounded. That of theR

ISSN:0319-5724    

DOI:10.2307/3315416

出版商:Wiley‐Blackwell    

年代:1990

数据来源: WILEY

摘要:

AbstractFor estimating powers of the generalized variance under a multivariate normal distribution with an unknown mean, the inadmissibility of the closest affine equivariant estimator is shown for the Pitman closeness criterion.

ISSN:0319-5724    

DOI:10.2307/3315417

出版商:Wiley‐Blackwell    

年代:1990

数据来源: WILEY

摘要:

AbstractPincus (1975) derived the null distribution of the likelihood‐ratio test statistic for testing that the mean vector of a multivariate normal distribution is zero against the alternative that the mean vector lies in a circular cone. Under the null hypothesis, the likelihood‐ratio test statistic has a chi‐bar‐squared distribution. We extend the results of Pincus by deriving the distribution of the likelihood‐ratio test statistic under the alternative hypothesis. In a special case, the distribution is a “noncentral chi‐bar‐squared” distribution. To our knowledge, this is the first order‐restricted testing problem for which the relationship between the null and alternative distributions of the test statistic is similar to the relationship in the linear‐model setting. That is, the distribution of the likelihood‐ratio test has a central form of a distribution under the null hypothesis and a noncentral form of the same distributio

ISSN:0319-5724    

DOI:10.2307/3315418

出版商:Wiley‐Blackwell    

年代:1990

数据来源: WILEY

摘要:

AbstractWe study the problem of testing: H0: μ ∈ P against H1: μ ∉ P, based on a random sample ofNobservations from ap‐dimensional normal distribution Np(μ, Σ) with Σ>0 and P a closed convex positively homogeneous set. We develop the likelihood‐ratio test (LRT) for this problem. We show that the union‐intersection principle leads to a test equivalent to the LRT. It also gives a large class of tests which are shown to be admissible by Stein's theorem (1956). Finally, we give the α‐level cutoff p

ISSN:0319-5724    

DOI:10.2307/3315419

出版商:Wiley‐Blackwell    

年代:1990

数据来源: WILEY

摘要:

AbstractUsing Blackwell's definition for comparison of experiments, it is shown that some sets of positively dependent random variables are less informative than similar sets of independent random variables. It is also shown that the information content of symmetric multivariate normal random vectors with a common known variance increases as the common correlation coefficient decreases. Some results which compare members of two‐parameter exponential families are also include

ISSN:0319-5724    

DOI:10.2307/3315420

出版商:Wiley‐Blackwell    

年代:1990

数据来源: WILEY