摘要:

AbstractThe likelihood‐ratio test statistic for testing homogeneity of exponential means with an ordered alternative has a rather complex null distribution. Expressions for the mean and variance of its null distribution are derived, and the accuracy of a two‐moment chi‐squared approximation is studied. The coefficients needed to implement the approximation are tabled. The application of these results in testing for a constant versus a nondecreasing intensity in a nonhomogeneous Poisson process is also disc

ISSN:0319-5724    

DOI:10.2307/3314758

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY

摘要:

AbstractUsing a Bayesian approach, unconditional and conditional predictive testing procedures are proposed for the detection of discordant observations for the translated exponential distribution in the presence of censored observations.

ISSN:0319-5724    

DOI:10.2307/3314759

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY

摘要:

AbstractThe Bertrand paradox is that, whereas we can define in a unique way a point uniformly at random in the interior of a circle, uniformly random chords can be given a variety of competing specifications. This is generalized to spheres, and the distributions of the uniformly random line sections (chords) and plane sections (disks) are tabulated. This includes the large class which are constructed as uniformly random chords of uniformly random disk sections.

ISSN:0319-5724    

DOI:10.2307/3314760

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY

摘要:

AbstractThe completeness of the induced distribution of the convex hull of a random set of points drawn uniformly from a convex region seems not to have been noticed before. The result generalizes a well‐known result for dimension one. As a consequence, there exists a theory of best unbiased estimation for certain functionals of the convex region. For example, a best estimator of the centroid of the convex region can be constructed. This estimator is distinct from the centroid of the convex hull. Therefore another generalization of a property holding in dimension one, namely the unbiased‐ness of the centroid of the convex hull, is seen to f

ISSN:0319-5724    

DOI:10.2307/3314761

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY

摘要:

AbstractFamilles of asymptotic 100(1 – α)% level confidence bands for the survival function under the general random right‐censorship (GRC) model and the proportional‐hazards model of random right‐censorship, also known as the Koziol‐Green (KG) model, are developed. The family of bands under the GRC model is based on the well‐known product‐limit estimator (PLE), and this family is rich in that it contains as special cases the bands of Hall and Wellner (1980) and Gillespie and Fisher (1979), and more generally, the GF‐type and HW‐type bands of Csörgő and Horváth (1986), as well as new bands not previously studied. The familles of bands under the KG model are based on the maximum‐likelihood estimator ofFunder this particular model. We compare the PLE‐based bands and the MLE‐based bands under the KG model. This enables us to study the loss in efficiency of the former bands when used in a setting where they are not optimal. The notion of asymptotic relative width efficiency (ARWE), defined to be the limiting ratio of the sample sizes needed by the bands to achieve the same asymptotic widths, is employed to compare two bands. Through this efficiency measure it is shown that if the censoring parameter β is known, then the PLE‐based bands are highly inefficient relative to the MLE‐based bands when β is large. When β is not known, the MLE‐based bands are asymptotically conservative. Despite their conservatism, they still dominate the PLE‐based bands when β is not too small or equivalently when the degree of censoring is not too light. We also compare the various PLE‐based bands under the GRC model. The resulting information is valuable for evaluating competing PLE‐based bands. We illustrate the confidence bands by u

ISSN:0319-5724    

DOI:10.2307/3314763

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY

摘要:

AbstractAn important statistical problem is to construct a confidence set for some functionalT(P) of some unknown probability distributionP. Typically, this involves approximating the sampling distributionJn(P) of some pivot based on a sample of sizenfromP. A bootstrap procedure is to estimateJn(P) byJn(&Pcirc;n), where P̂nis the empirical measure based on a sample of sizenfromP. Typically, one has thatJn(P) andJn(P̂n) are close in an appropriate sense. Two questions are addressed in this note. AreJn(P) andJn(P̂n) uniformly close asPvaries as well? If so, do confidence statements aboutT(P) possess a corresponding uniformity property? In the caseT(P) = P, the answer to the first questions is yes; the answer to the second is no. However, bootstrap confidence statements aboutT(P) can be made uniform over a restricted, though large, class ofP. Similar results apply to other functionalT(

ISSN:0319-5724    

DOI:10.2307/3314764

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY

摘要:

AbstractLetSp ×phave a Wishart distribution with parameter matrix Σ andndegrees of freedom. We consider here the problem of estimating the precision matrix Σ−1under the loss functionsL1(σ) tr (σ) ‐ log |σ| andL2(σ) = tr (σ). James‐Stein‐type estimators have been derived for an arbitraryp. We also obtain an orthogonal invariant and a diagonal invariant minimax estimator under both loss functions. A Monte‐Carlo simulation study indicates that the risk improvement of the orthogonal invariant estimators over the James‐Stein type estimators, the Haff (1979) estimator, and the “testimator” given by Sinha and Ghos

ISSN:0319-5724    

DOI:10.2307/3314766

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY

摘要:

AbstractSrivastava (1980) has shown that Grubbs's (1950) test for a univariate outlier is robust against the effect of equicorrelation. In this note we extend Srivastava's result by giving a more general covariance structure, which relaxes both the covariance structure and the assumption of equal variances. We also show that under the more general covariance structure, the power of Grubbs's test, as well as the significance level, is identical to the independently and identically distributed case.

ISSN:0319-5724    

DOI:10.2307/3314767

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY

摘要:

AbstractSome generalized commutation matrices are defined and used to establish relationships between π‐products and Kronecker products. These are applied to obtain expectations of π‐products of random vectors and mat

ISSN:0319-5724    

DOI:10.2307/3314768

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY

ISSN:0319-5724    

DOI:10.2307/3314769

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY