摘要:

A shorttof a one dimensional probability distribution is defined to be an interval which has at least probabilitytand minimal length. The length of a show and its obvious estimator are significant measures of scale of a distribution and the corresponding random sample, respectively. In this note a non‐parametric asymptotic confidence interval for the length of the (uniqueness is assumed) shorttis established in the random censorship from the right model. The estimator of the length of the shorttis based on the product‐limit (PL) estimator of the unknown distribution function. The proof of the result mainly follows from an appropriate combination of the Glivenko‐Cantelli theorem and the functional central limit theorem for the PL esti

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1995.tb01451.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

It is well‐known that maximum likelihood estimators are asymptotically normal with covariance equal to the inverse Fisher information in smooth, finite dimensional parametric models. Thus they are asymptotically efficient. A similar phenomenon has been observed for certain infinite dimensional parameter spaces. We give a simple proof of efficiency, starting from a theorem on asymptotic normality of infinite dimensionalM‐estimators. The proof avoids the explicit calculation of the Fisher information. We also address Hadamard differentiability of the correspondingM‐functi

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1995.tb01452.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Consider a collection of Bernoulli random variables on the two dimensional integer lattice and define the lengthDof the side of the largest square consisting entirely of successes, which covers the origin of the lattice. The paper gives a method to evaluate the probability distribution function ofD. An analogous problem for the Poisson process on the plane is also considered.

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1995.tb01453.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

This paper describes a practical method for estimating multivariate densities using wavelets. As in kernel methods, wavelet methods depend on two types of parameters. On the one hand we have a functional parameter: the wavelet Ø (comparable to the kernelK) and on the other hand we have a smoothing parameter: the resolution index (comparable to the bandwidthh). Classically, we determine the resolution index with a cross‐validation method. The advantage of wavelet methods compared to kernel methods is that we have a technique for choosing the wavelet Ø among a fixed family. Moreover, the wavelets method simplifies significantly both the theoretical and the practical computati

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1995.tb01454.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

The making of statistical inferences in distributional form is conceptionally complicated because the epistemic ‘probabilities’ assigned are mixtures of fact and fiction. In this respect they are essentially different from ‘physical’ or ‘frequency‐theoretic’ probabilities. The distributional form is so attractive and useful, however, that it should be pursued. Our approach is In line with Walds theory of statistical decision functions and with Lehmann's books about hypothesis testing and point estimation: loss functions are defined, risk functions are studied, unbiasedness and equivariance restrictions are made, etc. A central theme is that the loss function should be ‘proper’. This fundamental concept has been explored by meteorologists, psychometrists, Bayesian statisticians, and others. The paper should be regarded as an attempt to reconcile various schools of statisticians. By accepting what we regard 88 good and useful in the various approaches we are trying to develop a non

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1995.tb01455.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

We solve Problem 234 in Statistica Neerlandica by introducing the concept of slantedness. Distributions with a decreasing Lebesgue density are slanted to the right. This is no longer true for distributions on a lattice with decreasing density. Both kinds of distributions have positive central odd moments.

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1995.tb01456.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

The logical structure of a questionnaire is formally defined. This structure essentially consists of a set of constraints that should be obeyed by the joint answers to the questions in the questionnaire. The computational complexity of several test procedures for checking the consistency of the logical structure of a questionnaire is discussed.

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1995.tb01457.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

We review ten years of work on semiparametric theory in statistics on the occasion of the recently published book by Bickel, Klaassen, Ritov and Wellner.

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1995.tb01458.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1995.tb01459.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY