摘要:

Given a random vector (X1,…, Xn) for which the univariate and bivariate marginal distributions belong to some specified families of distributions, we present a procedure for constructing families of multivariate distributions with the specified univariate and bivariate margins. Some general properties of the resulting families of multivariate distributions are reviewed. This procedure is illustrated by generalizing the bivariate Plackett (1965) and Clayton (1978) distributions to three dimensions. In addition to providing rich families of models for data analysis, this method of construction provides a convenient way of simulating observations from multivariate distributions with specific types of univariate and bivariate marginal distributions. A general algorithm for simulating random observations from these families of multivariate distributions is presented

ISSN:0361-0918    

DOI:10.1080/03610919508813257

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

摘要:

Stable random variables are used in economics, engineering, hydrology and physics to model situations where the underlying distributions are heavy tailed. Stable densities do not generally have explicit formula, even in one variable. This paper describes the steps necessary to calculate multivariate stable densities by numerically inverting the characteristic function. We give a program tocalculate two dimensional stable densites that uses a recent two dimensional adaptive quadratureroutine. Graphs of families of such densities are given for a range of values of a and various spectral measures

ISSN:0361-0918    

DOI:10.1080/03610919508813258

出版商:Marcel Dekker, Inc    

年代:1995

数据来源: Taylor

摘要:

The main objective of this paper is to develop an exact Bayesian technique that can be used to assign a multivariate time series realization to one of several autoregressive sources, with unknown coefficients and precision, that might have different orders. The foundation of the proposed technique is to develop the posterior mass function of a classification vector, in an easy form, using the conditional likelihood function. A multivariate time series realization is assigned to the multivariate autoregressive source with the largest posterior probability. A simulation study, with uniform prior mass function, is carried out to demonstrate the performance of the proposed technique and to test its adequacy in handling the multivariate classification problems. The analysis of the numerical results supports the adequacy of the proposed technique in solving the classification problems with multivariate autoregressive sources.

ISSN:0361-0918    

DOI:10.1080/03610919508813259

出版商:Marcel Dekker, Inc    

年代:1995

数据来源: Taylor

摘要:

When testing equality of means from two independent normal populations, many statisticians prefer heterogeneity tolerant tests. Moser, Stevens, and Watts described the noncentral density and a numerical integration algorithm for computing power. We present simple and accurate approximations for the power of the Satterthwaite test statistic. Two advantages accrue. First, the approximations substantially reduce the computational burden for tasks such as plotting power curves. Second, theapproximations substantially simplify the programming and thereby make power calculations more widely available. Four methods of power approximation are evaluated for test sizes of .001, .01, .05,and .10, sample sizes of 6 and 51, variance ratios of 1 and 10, and noncentrality parameters from 0 to 50 by 1. A method based on a ratio of expected values is recommended due to its accuracy and simplicity.

ISSN:0361-0918    

DOI:10.1080/03610919508813260

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

摘要:

A higher order approximation formula for a percentage point of the noncentral t–distribution with v degrees of freedom is given up to the order o(v-3), using the Cornish-Fisher expansion for the statistic based on a lin-ear combination of a normal random variable and a chi-random variable. The upper confidence limit and the confidence interval for the non–centrality parameter are given. Numerical results are also obtained.

ISSN:0361-0918    

DOI:10.1080/03610919508813261

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

摘要:

Simple algorithms are given to simulate samples from multimodal circu-lar distributions corresponding to the wrapped Cauchy distribution. These algorithms are used in a acceptance-rejection method to simulate samples from multimodal circular distributions of the von Mises type.

ISSN:0361-0918    

DOI:10.1080/03610919508813262

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

摘要:

We explore the sensitivity of the point estimates of the fixed effects and variance components, and of interval estimates and hypothesis tests of the fixed effects, to the distributional assumptions about the random effects in longitudinal data analysis using the REML estimation procedure described by Laird and Ware (1982). In the small sample setting we consider distributions for the random effects that differ in tail thickness and skewness from the assumed normality. We investigate the bias, mean square error of the point estimates of the fixed effects and the variance components, the actual coverage of the nominal normal theory (1-α)% confidence intevals for the fixed effects, and α-level hypotheses tests performance under an asymptotic criteria. When random effects are not normal, but symmetric, point and interval estimates of fixed effects are unaffected, but estimates of variance components are highly variable. When random effects are from a skewed distribution, REML performs quite poorly

ISSN:0361-0918    

DOI:10.1080/03610919508813263

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

摘要:

As it is well known, Ridge Regression can be a useful technique for estimating the coefficients of a Multiple Regression Model in the presence of multicollinearity. It has, however, the drawback that the distribution of the estimator is unknown, so that only asymptotic confidence intervals may be obtained. The aim of this paper is to report on the use of a technique that combines the Bootstrap and the Edgeworth Expansion to obtain an approximation to the distribution of some Ridge Regression estimators. Some simulation experiments were carried out to compare the asymptotic confidence intervals with those obtained with this technique

ISSN:0361-0918    

DOI:10.1080/03610919508813264

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

摘要:

The minimum disparity estimators proposed by Lindsay (1994) for discrete models form an attractive subclass of minimum distance estimators which achieve their robustness without sacrificing first order efficiency at the model. Similarly, disparity test statistics are useful robust alternatives to the likelihood ratio test for testing of hypotheses in parametric models; they are asymptotically equivalent to the likelihood ratio test statistics under the null hypothesis and contiguous alternatives. Despite their asymptotic optimality properties, the small sample performance of many of the minimum disparity estimators and disparity tests can be considerably worse compared to the maximum likelihood estimator and the likelihood ratio test respectively. In this paper we focus on the class of blended weight Hellinger distances, a general subfamily of disparities, and study the effects of combining two different distances within this class to generate the family of “combined” blended weight Hellinger distances, and identify the members of this family which generally perform well. More generally, we investigate the class of "combined and penal-ized" blended weight Hellinger distances; the penalty is based on reweighting the empty cells, following Harris and Basu (1994). It is shown that some members of the combined and penalized family have rather attractive properties

ISSN:0361-0918    

DOI:10.1080/03610919508813265

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

摘要:

In this article we compare and contrast finite algorithms for computing the noncentral x2distribution function for odd or even degrees of freedom with the algorithms proposed recently by Ashour & Abdel-Samad (1990). We also obtain an alternative error bound for Ruben's (1974a) algorithm for even degrees of freedom and analyze the rate of convergence of two common infinite series representations for computing the cdf

ISSN:0361-0918    

DOI:10.1080/03610919508813266

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor