摘要:

This article describes and illustrates a local instability that may arise when using the method of least median squares (LMS) to fit models to data. This idea is contrary to the generally held belief that the method is highly resistant to perturbations in the data. In fact, slight changes in centrally located data can cause the LMS estimate to change by a large amount. The LMS method uses a criterion function that is calculated on half samples. If there are two or more half-samples with roughly the same value of the criterion function, then by slight changes in some of the data the LMS solution can be made to jump from one half sample to the other. An example of a data set from a standard text that exhibits this feature is presented. This suggests that some caution should be exercised when using this method. It does not automatically guarantee complete robustness to misspecifications in the data.

ISSN:0003-1305    

DOI:10.1080/00031305.1992.10475855

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Even to the initiated, statistical calculations based on Bayes's Theorem can be daunting because of the numerical integrations required in all but the simplest applications. Moreover, from a teaching perspective, introductions to Bayesian statistics—if they are given at all—are circumscribed by these apparent calculational difficulties. Here we offer a straightforward sampling-resampling perspective on Bayesian inference, which has both pedagogic appeal and suggests easily implemented calculation strategies.

ISSN:0003-1305    

DOI:10.1080/00031305.1992.10475856

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

ISSN:0003-1305    

DOI:10.1080/00031305.1992.10475857

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Use and implementation of the complementary log regression model are discussed, integrating various separate applications of the model under the form of a generalized linear model. Some motivation is drawn from cases where an underlying random variable is reduced to a dichotomous form. Estimation and testing are facilitated by recognizing the complementary log as a specific link function within a generalized linear framework. Testing for goodness of link via efficient scores is also discussed.

ISSN:0003-1305    

DOI:10.1080/00031305.1992.10475858

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

The 1987 National Medical Expenditure Survey (NMES) included an initial screener interview to facilitate the oversampling of groups of particular policy interest: Blacks, Hispanics, the poor and near poor, the elderly, and persons with functional limitations. Although households were then selected based on the characteristics of their members, the sampling unit for the first round of NMES data collection was the household address. The first core interview was then conducted with persons residing at the sample address at the time of the interview, whether or not they lived there at the time of the screening interview. This article examines the consequences of this strategy in terms of meeting specified survey design goals.

ISSN:0003-1305    

DOI:10.1080/00031305.1992.10475859

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

In this departmentThe American Statisticianpublishes articles, reviews, and notes of interest to teachers of the first mathematical statistics course and of applied statistics courses. The department includes the Accent on Teaching Materials section; suitable contents for the section are described under the section heading. Articles and notes for the department, but not intended specifically for the section, should be useful to a substantial number of teachers of the indicated types of courses or should have the potential for fundamentally affecting the way in which a course is taught.

ISSN:0003-1305    

DOI:10.1080/00031305.1992.10475860

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

The standard textbook presentations of moment computations for the geometric distribution involve, in one way or another, an application of the calculus. In this article, certain graphical representations of infinite series are used to facilitate direct and elementary derivation of these moments.

ISSN:0003-1305    

DOI:10.1080/00031305.1992.10475861

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

LetXdenote the number of itemsdeclareddefective in a sample of sizenselected without replacement from a batch ofNitems containing θ defectives, where testing is fallible. In this note it is shown that the density ofX,p(x, θ), has a monotone likelihood ratio (MLR) inx, and the relevance of this fact to inference is discussed in detail. In addition, an interesting connection is made between the MLR property and the suitability ofXas a proxy for the “true” number of defectives in regression modeling.

ISSN:0003-1305    

DOI:10.1080/00031305.1992.10475862

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

The problem of estimating the probability of an odd number of successes innindependent Bernoulli trials in minimum variance unbiased fashion is addressed. It is shown that this single problem, which arises naturally in elementary communications engineering applications, generates examples of several important aspects of parametric estimation theory.

ISSN:0003-1305    

DOI:10.1080/00031305.1992.10475863

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

A bivariate change of variable is proposed that elucidates the major distributional identities involving the two beta distributions and the chi-squared distribution. These identities are then seen to be the consequence of simple trigonometric relationships. The extension tondimensions clarifies further identities. There are, however, identities that seem not to fit into this scheme; three of these are reported.

ISSN:0003-1305    

DOI:10.1080/00031305.1992.10475864

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor