摘要:

Reduced rank approximation of matrices has hitherto been possible only by unweighted least squares. This paper presents iterative techniques for obtaining such approximations when weights are introduced. The techniques involve criss-cross regressions with careful initialization. Possible applications of the approximation are in modelling, biplotting, contingency table analysis, fitting of missing values, checking outliers, etc.

ISSN:0040-1706    

DOI:10.1080/00401706.1979.10489819

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

The rank transform is a simple procedure which involves replacing the data with their corresponding ranks. The rank transform has previously been shown by the authors to be useful in hypothesis testing with respect to experimental designs. This study shows the results of using the rank transform in regression. Two sets of data given by Daniel and Wood [8] are considered for purposes of illustrating the rank transform in simple and multiple regression. Also given are the results of a Monte Carlo study which compares regression on ranks with some published Monte Carlo results on isotonic regression. This Monte Carlo study is also modified to compare regression on ranks with robust regression. Another illustration gives the results of analyses on large computer codes by regression on ranks. The rank transform is a simple, repeatable process that compares favorably with other methods such as given by Andrews [1]. Our studies indicate the method works quite well on monotonic data.

ISSN:0040-1706    

DOI:10.1080/00401706.1979.10489820

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

The problem of estimating parameters of a linear model in the presence of extraneous estimates of a parameter subset is considered. Two approaches are considered; one augments the linear model with the extra information and the second reduces the dimension and estimates only the remaining parameters. It is shown that the two approaches yield identical estimates of the unspecified parameter subset. In situations where one is interested only in the estimation of the unspecified parameter subset, computational advantages of the reduced model over the augmented model are pointed out. Application of such estimation to aircraft tracking in meteorological experiments is given.

ISSN:0040-1706    

DOI:10.1080/00401706.1979.10489821

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

This article reviews the practical aspects of several nonparametric subset selection rules useful in block design problems, and discusses advantages and disadvantages of these methods. The populations are assumed stochastically ordered by the parameter of interest. Rules based on ranked observations are given for selecting a subset of populations which contains, with a specified confidence level, the population characterized by the smallest (or largest) parameter value. These procedures are applied to state traffic fatality rates recorded yearly (1960-76). New England states and Middle Atlantic states comprise most of the subset asserted, with a 90% confidence level, to contain the state with the smallest fatality rate; whereas, Southern states, Southwestern states and Rocky Mountain states generally comprise the subset for the state with the largest fatality rate.

ISSN:0040-1706    

DOI:10.1080/00401706.1979.10489822

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

A nonrandomized sign test is described that is less conservative than the commonly prescribed, and used, sign test for experiments in which neutral responses are possible. Tables of critical values are given for the new one-sided test with α = 0.01 and 0.05 (which can also be used for two-sided tests with α = 0.02 and 0.10).

ISSN:0040-1706    

DOI:10.1080/00401706.1979.10489823

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

Sometimes the problem of data classification arises without any knowledge of the underlying classes. Furthermore, not enough sample data from the classes may be available to develop reliable parametric estimates and, hence, data classification rules. However, when the size of the mixed data to be classified is large, computer aided techniques for displaying data with histograms and frequency tables can be exploited to compensate partially for the lack of class knowledge and sample data. Based on this concept, a numerical classification procedure is developed and is described in this paper. The classification rule is completely data directed and utilizes the data marginal distributions in a sequential manner. The technique was employed for partitioning certain remotely sensed multispectral scanner data for a number of sites in the U.S. and was found to be fairly competitive when compared to some commonly used parametric approaches utilizing training sample data.

ISSN:0040-1706    

DOI:10.1080/00401706.1979.10489824

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

In some life testing situations the minimum life can be nonzero. This paper develops O.C. curves for a hypothesis test concerning the minimum life where the underlying failure distribution is exponential. The O.C. curves provide a rational means for sample size decisions such that the Type II error is controlled. The effects of unknowingly applying this hypothesis test to a non-exponential distribution are also briefly assessed.

ISSN:0040-1706    

DOI:10.1080/00401706.1979.10489825

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

A production process is assumed to producektypes of items in varying proportions and with varying defect rates. This paper proposes a sequential inspection plan which allows one to optimally allocate inspection resources so that one obtains a good estimate of average quality. The plan is fairly easy to put into practice and allows for easy modification should production characteristics change.

ISSN:0040-1706    

DOI:10.1080/00401706.1979.10489826

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

In this paper the outgoing quality and the total inspection under sampling for attributes are introduced as well-defined random variables. The variances of these random variables under total rectification are presented and are depicted graphically.

ISSN:0040-1706    

DOI:10.1080/00401706.1979.10489827

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

Bowden and Graybill construct uniform confidence bands under the familiar simple linear regression model, and use those bands to write joint confidence intervals forexpected YgivenX=Xofor allXoin a specified finite rangeXa≤Xo≤Xb. Their approach is extended here to provide joint confidence intervals forindividualobservations onYgivenX, and also forindividual XgivenY(the inverse interval estimation problem), in both cases using uniform confidence bands constructed forXa≤X≤Xb. We show that Bowden and Graybill's tables can be used in these applications, and give supplementary tables to cover additional cases which more commonly arise in these new contexts. Asymptotic results are also given, allowing the user to generate additional “table” values.

ISSN:0040-1706    

DOI:10.1080/00401706.1979.10489828

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor