摘要:

Measures of the probability of all unobserved species are applied to the problem of assessing the adequacy of a search for a global maximum using random starting points. The measures, as used here, estimate the probability that an iterative algorithm using a randomly selected starting point will find a solution not observed in previous random starting points. The probability of an unobserved global maximum is less than or equal to this probability. We used these measures to evaluate the adequacy of our search procedure for the maximum likelihood estimates of the parameters of a mixture of two normals. These measures indicated that for most problems generated there was little chance that there were unobserved domains of convergence. Occasional problems, however, had appreciable estimated probabilities. In such problems, examination of the data suggested regions where a more focused search for unobserved domains of convergence was warranted.

ISSN:0162-1459    

DOI:10.1080/01621459.1989.10478867

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Matching is a common method of adjustment in observational studies. Currently, matched samples are constructed using greedy heuristics (or “stepwise” procedures) that produce, in general, suboptimal matchings. With respect to a particular criterion, a matched sample is suboptimal if it could be improved by changing the controls assigned to specific treated units, that is, if it could be improved with the data at hand. Here, optimal matched samples are obtained using network flow theory. In addition to providing optimal matched-pair samples, this approach yields optimal constructions for several statistical matching problems that have not been studied previously, including the construction of matched samples with multiple controls, with a variable number of controls, and the construction of balanced matched samples that combine features of pair matching and frequency matching. Computational efficiency is discussed. Extensive use is made of ideas from two essentially disjoint literatures, namely statistical matching in observational studies and graph algorithms for matching. The article contains brief reviews of both topics.

ISSN:0162-1459    

DOI:10.1080/01621459.1989.10478868

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

On April 1, 1990, the decennial census for the United States will be conducted by the U.S. Bureau of the Census. By December 31, 1990, the Census Bureau is specified by law to submit state population counts for the purpose of reapportionment of the U.S. House of Representatives, and by March 31, 1991, to submit small-area population counts for the purpose of redistricting. Census counts are used in a variety of other ways: for revenue-sharing formulas between different levels of government, for demographic projections, as a base for morbidity and mortality statistics, and so forth. Inaccurate census counts should be cause for concern for the whole nation. It is universally acknowledged that certain groups of people (e.g., young black males, illegal aliens, etc.) are harder to count than others. If the hard-to-count groups are distributed in equal proportions throughout the United States, there would be far less controversy over what to do about the uncounted people. As it is, many large American cities such as Chicago, Detroit, New York, and Los Angeles feel they are losing federal funds because their cities contain larger numbers of the groups that are less well counted. And certain states such as New York and California feel they are underrepresented in Congress, to the benefit of Midwestern states such as Indiana and Iowa. Census undercount is defined simply as the difference between the true count and the census count, expressed as a percentage of the true count. Small-area estimation of this undercount is considered here, using empirical Bayes methods based on a new and, it is argued, more realistic model than has been used before. Grouping of like subareas from areas such as states, counties, and so on into strata is a useful way of reducing the variance of undercount estimators. By modeling the subareas within a stratum to have a common mean and variances inversely proportional to their census counts, and by taking into account sampling of the areas (e.g., by dual-system estimation), empirical Bayes estimators that compromise between the (weighted) stratum average and the sample value can be constructed. The amount of compromise is shown to depend on the relative importance of stratum variance to sampling variance. These estimators are evaluated at the state level (51 states, including Washington, D.C.) and stratified on race/ethnicity (3 strata) using data from the 1980 postenumeration survey (PEP 3–8, for the noninstitutional population).

ISSN:0162-1459    

DOI:10.1080/01621459.1989.10478869

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Distribution-free tests are investigated for the one-sample multivariate location problem. Counts, called interdirections, which measure the angular distance between two observation vectors relative to the positions of the other observations, are introduced. These counts are invariant under nonsingular linear transformations and have a small-sample distribution-free property over a broad class of population models, called distributions with elliptical directions, which includes all elliptically symmetric populations and many skewed populations. A sign test based on interdirections is described, including, as special cases, the two-sided univariate sign test and Blumen's bivariate sign test. The statistic is shown to have a limiting χ2pnull distribution and, because it is based on interdirections, it is also seen to be invariant and to have a small-sample distribution-free property. Pitman asymptotic relative efficiencies and a Monte Carlo study show the test to perform well compared with Hotelling'sT2, particularly when the underlying population is heavy-tailed or skewed. In addition, it consistently outperforms the component sign test, which is often recommended in the nonparametric literature.

ISSN:0162-1459    

DOI:10.1080/01621459.1989.10478870

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A method is proposed for approximating the marginal posterior density of a continuous function of several unknown parameters, thus permitting inferences about any parameter of interest for nonlinear models when the sample size is finite. Possibly tedious numerical integrations are replaced by conditional maximizations, which are shown to be quite accurate in a number of special cases. There are similarities with the profile likelihood ideas originated by Kalbfleisch and Sprott (1970), and the method is contrasted with a Laplacian approximation recommended by Kass, Tierney, and Kadane (1988, in press), referred to here as the “KTK procedure.” The methods are used to approximate the marginal posterior densities of the log-linear interaction effects and an overall measure of association in a two-way contingency table. Snee's (1974) hair/eye color data are reanalyzed, and adjustments are proposed to Goodman's (1964) analysis for the full-rank interaction model. Another application concerns marginalization problems for a discretep-parameter exponential family distribution, and inferences are considered for the probability of a zero count.

ISSN:0162-1459    

DOI:10.1080/01621459.1989.10478871

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

This article considers the problems of testing additivity and estimating σ2in unreplicated multiway classifications. To model nonadditivity and jointly estimate σ2, the interaction parameter space must be restricted; otherwise the model is saturated. The parameterization we use is a multiway extension of the two-way multiplicative interaction model of Mandel (1971) and Johnson and Graybill (1972a). For example, in a three-way classification, we model interaction asθijk= λδ1iδ2jδ3k. This structure is a special case of thek-mode principal components model, which has received considerable attention in the psychometric literature (Kapteyn, Neudecker, and Wansbeek 1986). We construct an exact test of λ = 0 and propose an estimator of σ2that can be used when interaction has been detected. Our test is an approximation to the likelihood ratio test (LRT) ofHo: λ = 0. The proposed test has essentially the same power as the LRT but is easier to compute, and the exact null distribution of the test statistic is known. Selected percentiles of the null distribution are given for three-way classifications. For large |λ/σ|, a transformation of the test statistic is shown to be approximately distributed as a noncentralFand can be used to compute the power of the test. The test and estimator are illustrated on a data set having three rows, three columns, and four layers.

ISSN:0162-1459    

DOI:10.1080/01621459.1989.10478872

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Many survival studies record the times to two or more distinct failures on each subject. The failures may be events of different natures or may be repetitions of the same kind of event. In this article, we consider the regression analysis of such multivariate failure time observations. Each marginal distribution of the failure times is formulated by a Cox proportional hazards model. No specific structure of dependence among the distinct failure times on each subject is imposed. The regression parameters in the Cox models are estimated by maximizing the failure-specific partial likelihoods. The resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated. Simultaneous inferential procedures are then proposed. Extensive Monte Carlo studies indicate that the normal approximation is adequate for practical use. The new methods allow time-dependent covariates, missing observations, and arbitrary patterns of censorship. They are illustrated with two real-life examples. For recurrent failure time data, various regression methods have been proposed in the literature. These methods, however, generally assume stringent structures of dependence among the recurrences of each subject. Moreover, as shown in the present article, they are rather sensitive to model misspecification.

ISSN:0162-1459    

DOI:10.1080/01621459.1989.10478873

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

We derive the asymptotic distribution of the maximum partial likelihood estimator β for the vector of regression coefficients β under a possibly misspecified Cox proportional hazards model. As in the parametric setting, this estimator β converges to a well-defined constant vector β*. In addition, the random vectorn1/2(β – β*) is asymptotically normal with mean 0 and with a covariance matrix that can be consistently estimated. The newly proposed robust covariance matrix estimator is similar to the so-called “sandwich” variance estimators that have been extensively studied for parametric cases. For many misspecified Cox models, the asymptotic limit β* or part of it can be interpreted meaningfully. In those circumstances, valid statistical inferences about the corresponding covariate effects can be drawn based on the aforementioned asymptotic theory of β and the related results for the score statistics. Extensive studies demonstrate that the proposed robust tests and interval estimation procedures are appropriate for practical use. In particular, the robust score tests perform quite well even for small samples. In contrast, the conventional model-based inference procedures often lead to tests with supranominal size and confidence intervals with rather poor coverage probability.

ISSN:0162-1459    

DOI:10.1080/01621459.1989.10478874

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Data from a classical Pareto distribution are to be used to make inferences about the inequality and precision parameters. In addition, it is desired to predict the behavior of further observations from the distribution. Three typical data configurations are considered (iid and two types of censoring). Dependent conjugate prior analyses are reviewed and are compared with an analysis involving independent priors for the inequality and precision parameters. It is argued that mathematical tractability should be, perhaps, a minor consideration in the choice of priors. A comparative example is included.

ISSN:0162-1459    

DOI:10.1080/01621459.1989.10478875

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A new result dealing with smoothing and interpolation in the state-space model is developed and explored. The result simplifies the derivation of existing smoothing algorithms and provides alternate forms that have analytic and practical computing advantages. The connection to signal extraction and interpolation is explored, and diffuse specifications are considered.

ISSN:0162-1459    

DOI:10.1080/01621459.1989.10478876

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor