摘要:

This article focuses primarily on a comparison between the reference priors of Berger and Bernardo and the reverse reference priors suggested by J. K. Ghosh. Sufficient conditions are given that provide agreement between the two classes of priors. Several examples are given showing the agreement or disagreement between the two. In addition, these priors are compared under a criterion that requires the frequentist coverage probability of the posterior region of a real-valued parametric function to match a nominal level with a remainder ofO(n−1), wherendenotes the sample size. The latter priors, first introduced by Welch and Peers, are obtained by solving a differential equation due to Peers. Finally, in the presence of several parameters of interest, a general class of priors that satisfies the matching criterion separately for each parameter is constructed, and examples are given to illustrate how reference or reverse reference priors fit within this class of priors.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476640

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

We develop an improved empirical Bayes estimation methodology for the analysis of two-state Markov chains observed from heterogeneous individuals. First, the two transition probabilities corresponding to each chain are assumed to be drawn from a common, bivariate distribution that has beta marginals. Second, randomly missing observations are incorporated into the likelihood for the hyperparameters by efficiently summing over all possible values for the missing observations. A likelihood ratio test is used to test for dependence between the transition probabilities. Posterior distributions for the transition probabilities are also derived, as is an approximation for the equilibrium probabilities. The proposed procedures are illustrated in a numerical example and in an analysis of longitudinal store display data.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476641

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

In measuring visual acuity, the extremes of a set of normally distributed measures are of concern, together with one or more covariates. This leads to a model in which (X, Y1,Y2) are jointly normally distributed withY1,Y2exchangeable and (X, Yi) having a common correlation. Inferential procedures are developed for correlations and linear regressions amongXand the orderedYvalues. This requires determination of the covariance matrix ofX, Y(1)= min{Y1,Y2} andY(2)= max{Y1,Y2}. The inadequacy of certain estimates that ignore the nonnormality of {X, Y(1),Y(2)} is also discussed. Although the bivariate case is emphasized because of the context of the visual acuity model, many results are given for the more general multivariate case.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476642

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

This article uses the concept of data depth to introduce several new control charts for monitoring processes of multivariate quality measurements. For any dimension of the measurements, these charts are in the form of two-dimensional graphs that can be visualized and interpreted just as easily as the well-known univariateX, X, and CUSUM charts. Moreover, they have several significant advantages. First, they can detect simultaneously the location shift and scale increase of the process, unlike the existing methods, which can detect only the location shift. Second, their construction is completely nonparametric; in particular, it does not require the assumption of normality for the quality distribution, which is needed in standard approaches such as the χ2and Hotelling'sT2charts. Thus these new charts generalize the principle of control charts to multivariate settings and apply to a much broader class of quality distributions.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476643

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

A class of rank tests for analysis of variance based on linear functions of the Wilcoxon/Mann-Whitney statistics between cells is studied. This class includes many popular procedures. Assuming a location-family model, a condition for optimal Pitman efficacy of tests of main effects in this class is given. Tests for main effects in two-way layouts that achieve this optimality are shown to improve on previous proposals when the sample sizes are unbalanced. Nested orthogonal contrasts are introduced that can be used to decompose the overall test statistics into independent components to assess the contribution of individual contrasts. A new definition of interaction appropriate for rank-based analysis of variance is suggested, and test procedures are proposed.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476644

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

Confidence intervals for the survival function and the cumulative hazard function are considered. These confidence intervals are based on an inversion of the likelihood ratio statistic. To do this, two extensions of the likelihood, each of which yields meaningful likelihood ratio hypothesis tests and subsequent confidence intervals, are considered. The choice of the best extension is difficult. In the failure time setting, the binomial extension is best in constructing confidence intervals concerning the survival function and the Poisson extension is best in constructing confidence intervals concerning the cumulative hazard. Simulations indicate that these two methods perform as well as or better than competitors based on the asymptotic normality of the estimator.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476645

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

The problem of interest is the estimation of occurrence probabilities based on prevalent data in competing risks models. In the literature, the development of nonparametric methods has relied heavily on the independent competing risks assumption. The primary purpose of this article is to establish a statistical framework without excluding the possibility of dependence among competing risks. This is done through the use of crude hazard functions. The crude hazard functions not only are estimable regardless of whether the competing risks are independent, but also are mathematically more tractable. In this article we show that there is a one-to-one correspondence between the crude hazard functions and the occurrence probabilities. The general inversion formulas for the occurrence probabilities are presented, from which various representations can be derived under different sampling techniques. Maximum likelihood estimators are derived using these representations for nonparametric and length bias data. The maximum likelihood property and asymptotic behavior of both estimation procedures are studied. The simulation results show that the length bias estimators have smaller variances compared to the nonparametric estimators. Nevertheless, the nonparametric estimation procedure appears to be more robust to model assumptions.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476646

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

Although mixtures of decreasing failure rate (DFR) distributions are always DFR, some mixtures of increasing failure rate (IFR) distributions can also be ultimately DFR. In this article various types of discrete and continuous mixtures of IFR distributions are considered, and conditions are developed for such mixtures to be ultimately DFR. These conditions lead to an interesting result—that certain mixtures of IFR distributions, even those with very rapidly increasing failure rates (e.g., Weibull, truncated extreme), ultimately become DFR distributions. It is common practice to pool data from several different IFR distributions to enlarge sample size, for instance. The results of this article sound a warning that such pooling may actually reverse the IFR property of the individual samples to a DFR property.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476647

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

In a nonrandom sample or a nonrandomized comparison of treated and control groups, methods are developed for displaying the sensitivity of confidence intervals for population quantiles to the magnitude of the departure from random selection. Quantiles of a single distribution and for a shift in two distributions are both discussed. These confidence intervals are based on a new inequality for the distribution of the number of successes in a nonrandom sample or nonrandomized comparison. The inequality has additional applications. In particular, it greatly accelerates the computations in a sensitivity analysis for the Mantel–Haenszel statistic in a 2 × 2 ×Scontingency table. Examples include a nonrandom collection of blood samples from a town with comparatively high levels of radon gas, an observational study of chromosome damage from mercury, and a study of the drug allopurinol as a cause of skin rash. The proof of the inequality makes use of Savage's lattice for ranks and Holley's inequality, which gives sufficient conditions for stochastic ordering in a lattice.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476648

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

A moment method is proposed for regression analysis of bivariate ordered categorical data using the global odds ratio as the measure of association. For modeling the margins, this method utilizes the stochastic ordering implicit in the data. This method allows for covariate effects in modeling the association between responses. An application of the proposed model is illustrated using the ophthalmological data from the Wisconsin Epidemiologic Study of Diabetic Retinopathy for identifying risk factors among younger onset diabetics. This model is also extended to a longitudinal data setting with more than two repeated measures.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476649

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor