ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475188

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

A simple statistic is proposed to test the hypothesis that a sample comes from a distribution in the domain of attraction of the Gumbel distribution. It is based on the topkorder statistics and is a generalization of the Shapiro–Wilk goodness-of-fit statistic. The critical region of the test and its power against the alternative that the sample comes from a distribution in another domain of attraction are studied theoretically and by simulation. The power turns out to be superior to that of other tests previously proposed.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475189

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475190

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Many of the existing measures for influential subsets in univariate ordinary least squares (OLS) regression analysis have natural extensions to the multivariate regression setting. Such measures may be characterized by functions of the submatricesHIof the hat matrixH, whereIis an index set of deleted cases, andQI, the submatrix ofQ=E(ETE)−1ET, whereEis the matrix of ordinary residuals. Two classes of measures are considered:f(·)tr[HIQI(I−HI−QI)a(I−HI)b]andf(·)det[(I−HI−QI)a(I−HI)b], wherefis a scalar function of the dimensions of matrices andaandbare integers. These characterizations motivate us to consider separable leverage and residual components for multiple-case influence and are shown to have advantages in computing influence measures for subsets. In the recent statistical literature on regression analysis, much attention has been given to problems of detecting observations that, individually or jointly, exert a disproportionate influence on the outcome of univariate linear regression analysis and to assessing the influence of such cases, individually or jointly. By far the most popular approach is that of measuring the change in some feature of the analysis upon deletion of one or more of the cases. Various measures have been proposed that emphasize different aspects of influence on the regression. For a review of such methods, see Cook (1977, 1979), Belsley, Kuh, and Welsch (1980), Cook and Weisberg (1982), and Chatterjee and Hadi (1986, 1988). In this article we generalize some of the univariate measures of influence to the multivariate regression setting and then show that the generalized measures are special cases of two general classes of influence measures. There are other approaches to influence measures in regression diagnostics (see, for example, Cook 1986) that are not special cases of our general classes. The majority of the existing measures, however, are.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475191

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Unbalanced split-plot designs are considered, where the whole-plot treatments could be replicated an unequal number of times in the design, but each split-plot treatment occurs exactly once in every whole plot. Analysis of such designs is provided when the various effects could be fixed or random. In each case, valid exact tests and optimum invariant tests (whenever they exist) are derived for testing the significance of the various effects. In some cases optimum tests exist only under additional conditions on the design, and these conditions are specified for the various setups.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475192

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

The nonlinear model with variance components, which combines a nonlinear model for the mean with additive random effects, is applicable to split-plot and nested experiments. We propose two methods of estimation for the parameters of the nonlinear model for the mean: (1) estimated generalized least squares (EGLS), and (2) maximum likelihood (MLE) by the method of scoring. Using a generalization of Klimko and Nelson's theorem on strong consistency of least squares estimators, it is possible to show that both the MLE and the EGLS estimators are strongly consistent, asymptotically normal, and asymptotically efficient.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475193

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Assume that a random sample is drawn from a population with unknown number of classes and possibly unequal class probabilities. A nonparametric estimation technique is proposed to estimate the number of classes using the idea of sample coverage, which is defined as the sum of the cell probabilities of the observed classes. Since expected sample coverage can be well estimated, we were motivated to find its role in the estimation of the number of classes. This work generalizes the result of Esty to a nonparametric approach and extends Darroch and Ratcliff to incorporate the heterogeneity of the class probabilities. The coefficient of variation of the class sizes is shown to play an important role in the recommended estimation procedures. The performance of the proposed estimators is investigated by means of Monte Carlo simulations.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475194

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

The average derivative is the expected value of the derivative of a regression function. Kernel methods have been proposed as a means of estimating this quantity. The problem of bandwidth selection for these kernel estimators is addressed here. Asymptotic representations are found for the variance and squared bias. These are compared with each other to find an insightful representation for a bandwidth optimizing terms of lower order thann–1. It is interesting that, for dimensions greater than 1, negative kernels have to be used to prevent domination of bias terms in the asymptotic expression of the mean squared error. The extent to which the theoretical conclusions apply in practice is investigated in an economical example related to the so-called “law of demand.”

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475195

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

It is well known that data-driven regression smoothing parametersħbased on cross-validation and related methods exhibit a slow rate of convergence to their optimum. In an earlier article we showed that this rate can be as slow asn–1/10; that is, for a bandwidthħ0optimizing the averaged squared error,n1/10(ħ—ħ0)/ħ0tends to an asymptotic normal distribution. In this article we consider mean averaged squared error optimal bandwidthsh0. This (nonrandom) smoothing parameter can be approximated much faster. We use the technique of double smoothing to show that there is anħsuch that, under certain conditions,n1/2(ħ−h0)/h0tends to an asymptotic normal distribution.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475196

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

This article describes a generalized moments specification test of the semiparametric proportional hazards model of Cox. In contrast to other specification tests for this model, the generalized moments test is applicable in the presence of continuous explanatory variables and does not require assigning the data to predetermined cells. The results of a Monte Carlo investigation suggest that the generalized moments test has good finite-sample properties and that it is more powerful than other available tests for models with continuous explanatory variables when the alternative is an accelerated failure time model. The test is based on generalized residuals for the proportional hazards model. When the model is correct, the generalized residuals have asymptotically the (possibly censored) unit exponential distribution. The generalized moments are means of functions of the generalized residuals. The generalized moments have known values when the generalized residuals have the unit exponential distribution, and an asymptoticχ2statistic tests for whether the differences between sample analogs of the generalized moments and the known values are larger than can be explained by random sampling errors.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475197

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor