摘要:

Consistent estimators are derived for the age-specific and lifetime incidence rates of late-onset diseases from censored, biased samples, using a discrete time model and a traditional assumption for size-biased sampling. The estimators are alternatives to the so-called index case estimators often used by epidemiologists under similar circumstances. The asymptotic normality of the proposed estimators is established and an adaptation of Greenwood's formula is given for estimating and comparing their asymptotic variances. We show that index case estimators can be inconsistent and find a necessary and sufficient condition for their consistency. The results are applicable in the study of familial aggregation of diseases that are not manifest at birth when the sample consists of families identified through a family member who has the disease of interest. A survey of families of nursing home patients with a narrowly defined form of Alzheimer's disease, undertaken to clarify its mode of inheritance is an example of such a study. Our work shows a possible lack of consistency of the estimators obtained in that study and in other similar studies. Besides familial aggregation, the results may also be applicable to the study of slowly working environmental causes of a disease insofar as they affect individuals as members of special groups, identified through some of their diseased members; for example, factory workers exposed to certain toxic materials.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476951

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The classical maximum entropy (ME) approach to estimating the unknown parameters of a multinomial discrete choice problem, which is equivalent to the maximum likelihood multinomial logit (ML) estimator, is generalized. The generalized maximum entropy (GME) model includes noise terms in the multinomial information constraints. Each noise term is modeled as the mean of a finite set of a priori known points in the interval [−1,1] with unknown probabilities where no parametric assumptions about the error distribution are made. A GME model for the multinomial probabilities and for the distributions associated with the noise terms is derived by maximizing the joint entropy of multinomial and noise distributions, under the assumption of independence. The GME formulation reduces to the ME in the limit as the sample grows large or when no noise is included in the entropy maximization. Further, even though the GME and the logit estimators are conceptually different, the dual GME model is related to a generalized class of logit models. In finite samples, modeling the noise terms along with the multinomial probabilities results in a gain of efficiency of the GME over the ME and ML. In addition to analytical results, some extensions, sampling experiments, and an example based on real-world data are presented.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476952

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

A simple test for multivariate normal data is proposed that has good power for alternatives where the mean vector tends to be positive. The test rejects if the quadratic form of the sample mean vector exceeds its 2α critical value and the sum of the elements of the mean vector exceeds zero. The proposed test is shown to have type I error rate equal to α whether or not the covariance matrix is known. Tight bounds on the power of the proposed test are provided, and the test is compared to three likelihood ratio tests.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476953

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

An extension of the concept of quantiles in multidimensions that uses the geometry of multivariate data clouds has been considered. The approach is based on blending as well as generalization of the key ideas used in the construction of spatial median and regression quantiles, both of which have been extensively studied in the literature. These geometric quantiles are potentially useful in constructing trimmed multivariate means as well as many otherLestimates of multivariate location, and they lead to a directional notion of central and extreme points in a multidimensional setup. Such quantiles can be defined as meaningful and natural objects even in infinite-dimensional Hilbert and Banach spaces, and they yield an effective generalization of quantile regression in multiresponse linear model problems. Desirable equivariance properties are shown to hold for these multivariate quantiles, and issues related to their computation for data in finite-dimensional spaces are discussed.n1/2consistency and asymptotic normality of sample geometric quantiles estimating the corresponding population quantiles are established after deriving a Bahadur-type linear expansion. The sampling variation of geometric quantiles is carefully investigated, and estimates for dispersion matrices, which may be used in developing confidence ellipsoids, are constructed. In course of this development of sampling distributions and related statistical properties, we observe several interesting facts, some of which are quite counterintuitive. In particular, many of the intriguing properties of spatial medians documented in the literature appear to be inherited by geometric quantiles.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476954

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The article extends the usual Lorenz curve and Lorenz order of univariate distributions to the multivariate case. For a given probability distribution in nonnegativedspace,d≥ 1, we define and investigate the Lorenz zonoid and the Lorenz surface, which are sets in (d+ 1) space. The surface equals the usual Lorenz curve whend= 1. Included is the definition of the Lorenz surface of a finite number of vectors that may be interpreted as the endowments of economic units indcommodities. As a notion of increasing multivariate disparity, we introduce the set inclusion of Lorenz zonoids and show that it is equivalent to directional majorization.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476955

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

A critical issue for users of Markov chain Monte Carlo (MCMC) methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest. Research into methods of computing theoretical convergence bounds holds promise for the future but to date has yielded relatively little of practical use in applied work. Consequently, most MCMC users address the convergence problem by applying diagnostic tools to the output produced by running their samplers. After giving a brief overview of the area, we provide an expository review of 13 convergence diagnostics, describing the theoretical basis and practical implementation of each. We then compare their performance in two simple models and conclude that all of the methods can fail to detect the sorts of convergence failure that they were designed to identify. We thus recommend a combination of strategies aimed at evaluating and accelerating MCMC sampler convergence, including applying diagnostic procedures to a small number of parallel chains, monitoring autocorrelations and cross-correlations, and modifying parameterizations or sampling algorithms appropriately. We emphasize, however, that it is not possible to say with certainty that a finite sample from an MCMC algorithm is representative of an underlying stationary distribution.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476956

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Bayesian TheoryJ. M. Bernardo, Adrian F. M. Smith, New York: John Wiley, 1994. 586 pp. $84.95. James M. Dickey, Morris L. Eaton, University of Minnesota

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476957

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Continuous Univariate Distributions, Vol. II (2nd ed.).Norman L. Johnson, Samuel Kotz, N. Balakrishnan., New York: John Wiley, 1995. xix + 719 pp. $85.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476958

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Marden, John I., and Muyot, Maria Emerita T., “Rank Tests for Main and Interaction Effects in Analysis of Variance,” 90 (December 1995), 1388–1398

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476959

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

This article has no abstract

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476900

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor