摘要:

For a two-parameter exponential model with increasing failure rate (IFR) or decreasing failure rate (DFR) distributions necessary and sufficient conditions of the existence of a solution of the likelihood equations are given. Also, all of the scale-invariant two-parameter statistical models closed by raising to a power and by exponential tilting are introduced. The conditions of existence of a solution of the likelihood equations are studied for these invariant models, and the models are applied to obtain some uniformly most powerful unbiased tests of exponentially against alternatives in these models.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474146

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

We show that the likelihood ratio test of exponentiality against singly truncated normal alternatives is the uniformly most powerful unbiased test and can be expressed in terms of the sampling coefficient of variation. This test is closely related to Greenwood's statistic for testing departures from the uniform distribution. We provide a way to approximate the critical points of the test, using saddlepoint methods, that gives a high degree of accuracy.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474147

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

A saddlepoint approximation is provided for the distribution function of oneMstatistic conditional on anotherMstatistic. Many interesting statistics based on dependent quantities (e.g., spacings, multinomial frequencies, rank differences) can be expressed in terms of independent identically distributed random variables conditioned on their sum, so that this conditional saddlepoint approximation yields accurate approximations for the distribution of such statistics. This saddlepoint approximation can also be used in conditional testing, where nuisance parameters are eliminated by conditioning on sufficient statistics.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474148

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

Bayesian hypothesis testing for nonnested hypotheses is studied, using various “default” Bayes factors, such as the fractional Bayes factor, the median intrinsic Bayes factor, and the encompassing and expected intrinsic Bayes factors. The different default methods are first compared with each other and with thepvalue in normal one-sided testing, to illustrate the basic issues. General results for one-sided testing in location and scale models are then presented. The default Bayes factors are also studied for specific models involving multiple hypotheses. In particular, a multiple hypothesis testing example involving a sequential clinical trial is discussed. In most of the examples presented we also derive the intrinsic prior; this is the prior distribution, which, if used directly, would yield answers (asymptotically) equivalent to those for the given default Bayes factor.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474149

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

We consider the problems of image segmentation and classification, and image restoration when the true image is made up of a small number of (unordered) colors. Our emphasis is on both performance and speed; speed has become increasingly important for analyzing large images and multispectral images with many bands, processing large image databases, real-time or near realtime image analysis, and the online analysis of video. Bayesian image analysis provides an elegant solution to these problems, but it is computationally expensive, and the solutions it provides may be sensitive to unrealistic global properties of the models on which it is based. The ICM algorithm is faster and based on thelocalproperties of the models underlying Bayesian image analysis; parameter estimation is performed iteratively via pseudolikelihood. Mathematical morphology is faster again and is widely considered to perform well, but lacks a statistical basis; method selection (analogous to parameter estimation) is done in a rather ad hoc manner. We proposeBayesian morphology, a synthesis of these methods that attempts to combine the speed of mathematical morphology with the principled statistical basis of ICM. The key observation is that when the original image is discrete (or if an initial segmentation has been carried out), then, assuming a Potts model for the true scene and channel transmission noise, (1) the ICM algorithm is equivalent to a form of mathematical morphology and (2) the segmentation is insensitive to the precise values of the model parameters. Unlike in standard Bayesian images analysis and ICM, it is feasible to do maximum likelihood estimation of the parameters in this setting. For gray-level or multispectral images, we propose an initial segmentation based on the EM algorithm for a mixture model of the marginal distribution of the pixels. The resulting algorithm is much faster than ICM, with gains that increase for more bands and larger images, and has good performance in experiments and for real examples.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474150

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

Politis and Romano have put forth a general subsampling methodology for the construction of large-sample confidence regions for a general unknown parameter θ associated with the probability distribution generating the stationary sequenceX1,…,Xn. The subsampling methodology hinges on approximating the large-sample distribution of a statisticTn=Tn(X1,…,Xn) that is consistent for θ at someknownrate τn. Although subsampling has been shown to yield confidence regions for θ of asymptotically correct coverage under very weak assumptions, the applicability of the methodology as it has been presented so far is limited if the rate of convergence τnhappens to be unknown or intractable in a particular setting. In this article we show how it is possible to circumvent this limitation by (a) using the subsampling methodology to derive a consistent estimator of the rate τn, and (b) using the estimated rate to construct asymptotically correct confidence regions for θ based on subsampling.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474151

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

Transformation from a parametric family can improve the performance of kernel density estimation. In this article we give two data-driven estimators for the optimal transformation parameter. We demonstrate that multiple families of transformations can be used at the same time, and there can be benefits to iterating this process. The transformation scheme can be expected to first pick the right transformation family and then pick the optimal parameter. Insight as to the performance of the method comes from our analysis of a number of real datasets, two of which are included in this article. To illustrate the effectiveness and asymptotics of the transformation method, we also present results on one of the five target densities used in our simulation study. It is then proved that the Johnson family of transformations, when coupled with transformation-kernel density estimation, makes a wide variety of density shapes easier to estimate. The transformation method has overall better performance than the usual method and in many cases is much more effective.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474152

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

This article analyses the recently suggested particle approach to filtering time series. We suggest that the algorithm is not robust to outliers for two reasons: The design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution. Here we tackle the first of these problems.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474153

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

I consider a method for combining different classifiers to develop more effective classification rules. The proposed combined classifier, which turns out to be strongly consistent, is quite simple to use in real applications. It is also shown that this combined classifier is, (strongly) asymptotically, at least as good as any one of the individual classifiers. In addition, if one of the individual classifiers is already Bayes optimal (asymptotically), then so is the combined classifier.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474154

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

In earlier work, we presented a maximin power clustering criterion to partition observations into groups of near replicates. Specifically, the criterion selects near replicate clusters for use with Christensen's tests for orthogonal between and within cluster lack of fit. This article further explores implementation of this clustering criterion. In particular, a methodology is developed to determine a collection of candidate groupings to which the maximin power criterion can be applied.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474155

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor