摘要:

We consider the multiple linear regression modelyi=x′iβ+εi,i= 1, 2, …,n, with random carriers and focus on the estimation ofβ. This article's main contribution is to present an estimator that is affine, regression, and scale equivariant; has both a high breakdown point and a bounded influence function; and has an asymptotic efficiency greater than .95 versus least squares under Gaussian errors. We give conditions under which the estimator—a one-step generalMestimator that uses Schweppe weights and is based on a high breakdown initial estimator—satisfies these properties. The major conditions necessary for the estimator are (a) it must be based on a √n-consistent initial estimator with a 50% breakdown point, and (b) it must be based on a psi function that is odd, bounded, and strictly increasing. The advantage of this estimator over previous approaches is that it does not downweight high leverage points without first considering how they fit the bulk of the data. Methods of computing diagnostics and constructing Wald-type tests about β are given. We illustrate the features of the estimator on a data set with two regressors, showing how a good leverage point is not downweighted, whereas a bad leverage point is downweighted.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476352

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

A crucial problem in building a multiple regression model is the selection of predictors to include. The main thrust of this article is to propose and develop a procedure that uses probabilistic considerations for selecting promising subsets. This procedure entails embedding the regression setup in a hierarchical normal mixture model where latent variables are used to identify subset choices. In this framework the promising subsets of predictors can be identified as those with higher posterior probability. The computational burden is then alleviated by using the Gibbs sampler to indirectly sample from this multinomial posterior distribution on the set of possible subset choices. Those subsets with higher probability—the promising ones—can then be identified by their more frequent appearance in the Gibbs sample.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476353

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Motivated by Buckley and James' modification of the least squares procedure for censored regression data, we derive a score process that incorporates the time evolution and handles staggered entry data in a natural way. By censored regression data we mean that the responses are subject to a possible right censorship. Such cases often arise from clinical trials and industrial life tests. The score process can be interpreted as a weighted comparison of (transformed) survival times. This is especially suitable for the accelerated failure time regression model. By expressing it in an appropriate form so that the counting process and its associate martingale theory can be applied, we show that the score process is approximated by a mean 0 multidimensional Gaussian process. A consistent estimator of its covariance matrix function is provided. Based on the covariance matrix estimator and the sequential test of Slud and Wei, a repeated significance test is then proposed. Usefulness of the procedure is illustrated with two well-known data sets: the beta-blocker heart attack trial data and the Stanford heart transplant data. Both data sets are also analyzed using the more familiar repeated log-rank test. Comparing results from the log-rank and the proposed tests shows that the two procedures tend to reach similar conclusions. Simulation studies are conducted to investigate the accuracy of the normal approximations when sample sizes are moderate and to compare efficiency with the commonly used log-rank statistic. The results indicate that the proposed test is superior when the underlying error distribution is normal, and the log-rank method is superior when the error distribution is extreme value. We also show how the proposed test can be modified to adjust for ancillary covariates.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476354

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The definition of a confidence interval is generalized so that problems such as constructing exact confidence regions for the difference in two normal means can be tackled without the assumption of equal variances. Under certain conditions, the extended definition is shown to preserve a repeated sampling property that a practitioner expects from exact confidence intervals. The proposed procedure is also applied to the problem of constructing confidence intervals for the difference in two exponential means and for variance components in mixed models. A repeated sampling property of generalizedpvalues is also given. With this characterization one can carry out fixed level tests of parameters of continuous distributions on the basis of generalizedpvalues. Finally, Pratt's paradox is revisited, and a procedure that resolves the paradox is given.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476355

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

This article considers the construction of an upper confidence bound on the range of a set ofklocation parameters, such as thektreatment effects in a one-way layout. This confidence bound will be useful to the experimenter in assessing the “equivalence” of the location parameters. Some general theoretical results are presented and the case of normally distributed data is considered in detail, with accompanying tables of confidence bounds. Some examples of the application of this new inference method are given.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476356

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

In many applications available data from several independent studies address the same question, and it is essential to have statistical methods for combining the results from the different studies. This article addresses this issue in two setups: (1) a testing hypothesis concerning the common mean vector of two independent linear models having different variances, and (2) a testing hypothesis concerning a common variance component in linear models involving two variance components. The interblock analysis of a balanced incomplete block design (BIBD) is a special case of (1) when we are interested in testing the equality of the treatment effects. Testing the significance of the treatment variance component in a BIBD with random effects is a special case of (2). We suggest some new test procedures for the testing problems in (1) and (2) and also give a review of the various existing tests. We numerically compare the powers of the various tests and make specific recommendations regarding the choice of the test to be used in practical applications.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476357

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

We consider a monotonicity problem concerning the critical values in stepwise multiple test procedures for comparingkparameters. This problem will be solved for a large class of distributional settings by means of an inequality for cumulative distribution functions of test statistics satisfying a simple monotonicity condition.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476358

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Single replicate designs are shown to be regular if and only if for each subset of factors there exists a partition of the corresponding treatment subcombinations such that, for each block, the treatment subcombinations in the block consist of the elements of one set of the partition equireplicated. Limitations of existing methods of confounding for single replicate designs are briefly discussed.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476359

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Consider an experiment where the factors are measured on a continuous scale, and suppose that the experimenter is permitted to augment the existing observations with one or more new data points. Bondar's universal optimality criterion (Uoptimality) suggests that the problem is best studied in the eigenvector coordinate system. We proceed by showing how to construct new points that first equate and then jointly increase the smaller eigenvalues of the crossproduct of the independent variables. We discuss the limitations of design augmentation strategies based solely on the crossproduct matrix. Our goals are to equate and minimize the variances of the estimated regression coefficients, keep the new points constrained in a prespecified experimental region, use as much of the information in the original points as possible, and keep the number of required new points as small as possible. We offer several data augmentation strategies to meet these requirements. AsUoptimality subsumes each of theD, A, E, and (M, S) optimality criteria, our strategies guarantee theU, D, A, E, and (M, S) optimality of the set of new points. The recommended number of additional points depends on how nearly optimal is the layout based on the existing observations and on the tightness of the regional constraints. We illustrate our strategies with a well-known experimental data set. For an additive model, ourU-optimal solutions to the data augmentation problem are superior to other solutions available in the literature.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476360

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The comparison of primary interest in a 2 × 2 crossover trial typically concerns the effect of the treatments, sayAandB, on the mean response level. This article deals with another important aspect, namely the within-subject response variability underAandB. Differences in drug formulation and/or administration may lead to considerable differences in within-subject variability, whatever the difference in terms of mean level. Consideration of both these aspects may, therefore, be of considerable importance for the judgement of the treatments. It is shown that although there are no within-subject treatment replications, it is possible to make various exact inferences about theA/Bratio of within-subject variances and about the (A – B)-difference in mean level, simultaneously and marginally. These inferences are semiparametric in that no distributional assumption is made about the between-subject variability, whereas a normality assumption is used for the within-subject variability. The inferences include tests, confidence regions, and a multiple test procedure. A power approximation is also given. The results are illustrated numerically.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476361

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor