摘要:

This paper is concerned with the computing needs of the mathematical statistician, doing his own research. It does not attempt a complete survey. Rather, two areas of relevance are looked at in some detail: the use of computer-aided mathematics and the simulation of probabilistic models. In each case we ask certain inter-related questions. What work has been done in the area, and how useful is it for statisticians? Given the present state of computing, what extensions of our current capability are feasible? In the process some of the author's work in the areas is described briefly.

ISSN:0040-1706    

DOI:10.1080/00401706.1970.10488630

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

“Current facilities for computing, display, and real time interaction have developed substantially beyond our understanding of how to use them effectively in data analysis. Current limitations in data analysis technology are mainly in explicating and organizing the science of data analysis and of defining and implementing the necessary associated computer software.

ISSN:0040-1706    

DOI:10.1080/00401706.1970.10488631

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

Stochastic networks and GERT, in particular, are used to analyze Reliability Problems. The advantages of the method are found to be (a) the flexibility of the logical nodes available in GERT, (b) the magnitude of information available from the system such as conditional network probabilities and times, counts on elements in the network and renewal times on the elements in the network, and (c) the ability to model complex reliability problems.

ISSN:0040-1706    

DOI:10.1080/00401706.1970.10488632

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

Confidence intervals forP(Y<X) are obtained under the assumptions thatXandYare independently normally distributed andt.he distribution ofYis known. The procedures of this paper are compared with a procedure suggested byZ. Govindarajulu.

ISSN:0040-1706    

DOI:10.1080/00401706.1970.10488633

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

In multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory, if not incorrect, if the prediction vectors are not orthogonal. Proposed is an estimation procedure based on adding small positive quantities to the diagonal ofX′X. Introduced is the ridge trace, a method for showing in two dimensions the effects of nonorthogonality. It is then shown how to augmentX′Xto obtain biased estimates with smaller mean square error.

ISSN:0040-1706    

DOI:10.1080/00401706.1970.10488634

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

This paper is an exposition of the use of ridge regression methods. Two examples from the literature are used as a base. Attention is focused on the RIDGE TRACE which is a two-dimensional graphical procedure for portraying the complex relationships in multifactor data. Recommendations are made for obtaining a better regression equation than that given by ordinary least squares estimation.

ISSN:0040-1706    

DOI:10.1080/00401706.1970.10488635

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

A number of criteria have been proposed for selecting the best subset or subsets of independent variables in linear regression analysis. Applying these criteria to all possible subsets is, in general, not feasible if the number of variables is large. Many of the criteria are monotone functions of the residual sum of squares hence the problem is reduced to identifying subsets for which this quantity is small.

ISSN:0040-1706    

DOI:10.1080/00401706.1970.10488636

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

The comparison of two measuring devices whose readings are subject to random variations involves 1) comparing their means to determine if they differ significantly and 2) comparing their variances to determine if they differ significantly. For the problem considered, the available data consist of one reading with one device and two additional independent readings with a second device on each of a number of units. An estimate of the difference in means can be readily obtained from the difference in the average readings for the two devices, and an estimate of the reading error variance for the second device is obtained from the differences in the two readings with that device. A method is also developed for estimating the reading error variance for the measuring device with only a single reading per unit. Procedures are given for testing hypotheses concerning the average difference in readings between the two devices, for testing the hypothesis that the reading error standard deviations are identical, for obtaining estimates of the standard deviations and for establishing confidence bounds. The methods are illustrated by an example and an extension of the problem is considered.

ISSN:0040-1706    

DOI:10.1080/00401706.1970.10488637

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

The present paper discusses some ranking and selection procedures for multivariate normal populations in terms of measures of dispersion. Using the generalized variance as the measure of dispersion, a procedure is defined to select a subset of the populations which would include the population with the smallest generalized variance with a certain probability. Two approximations to the distribution of the sample generalized variance are discussed. A discussion of the properties of the above procedure is also included.

ISSN:0040-1706    

DOI:10.1080/00401706.1970.10488638

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1970.10488639

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor