摘要:

Since much of the applied statistician's activity involves model fitting, it is proposed that estimation be approached from this view rather than from that of population inference based on assumed model families. To this end, estimation by the inversion of goodness of fit tests for completely specified models is considered. Several examples and some initial simulation results are given.

ISSN:0040-1706    

DOI:10.1080/00401706.1976.10489394

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

Three general purpose algorithms for maximum likelihood estimation of mean and variance components in mixed analysis of variance models are discussed. These are the Newton-Raphson algorithm, the Fisher scoring algorithm, and the Hemmerle and Hartley algorithm. Derivations for the first two are given and a unified presentation of all three makes some theoretical and practical comparisons possible. In addition the results of applying all three to a sequence of five problems are presented. TheWtransform of Hemmerle and Hartley is used throughout to reduce the computational burden associated with maximum likelihood variance component algorithms. The algorithms provide a unified approach to estimation and testing in the general mixed analysis of variance model.

ISSN:0040-1706    

DOI:10.1080/00401706.1976.10489395

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

A strategy for determining the most important components in a mixture system is developed. The proposed screening designs are usefrd in those situations where the number of candidate components,q, is large. Our simplex screening designs, which contain 2q+ 1 or 3q+ 1 points, are recommended when it is possible to experiment over the total composition range of all components (0–100%) or the experimental region can be expressed as a simplex in terms of pseudocomponents. We recommend extreme vertices screening designs, which contain approximatelyq+ 10 points, when some or all of the components are subject to upper and lower constraints. Examples are included to illustrate the proposed designs and associated analyses.

ISSN:0040-1706    

DOI:10.1080/00401706.1976.10489396

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

The maximum likelihood (ML) procedure of Hartley aud Rao [2] is modified by adapting a transformation from Pattersou and Thompson [7] which partitions the likelihood render normality into two parts, one being free of the fixed effects. Maximizing this part yields what are called restricted maximum likelihood (REML) estimators. As well as retaining the property of invariance under translation that ML estimators have, the REML estimators have the additional property of reducing to the analysis variance (ANOVA) estimators for many, if not all, cases of balanced data (equal subclass numbers).

ISSN:0040-1706    

DOI:10.1080/00401706.1976.10489397

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

Specific small sample properties are investigated for the two-way model with no interaction. It is observed that each of the usual ANOVA yields estimators with smaller variance in respective snbspaces of the parameter space. The design matrix role is related to both of these. Some representative numerical examples are given.

ISSN:0040-1706    

DOI:10.1080/00401706.1976.10489398

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

A simrdtaneous test, procedure is proposed for redrIcing the number of variables required to discriminate between two multivariate normal poprdatiorls. This procedure forms part of a wider simrdtaneolls procedure, for detailed descriptive analysis of group differences, which isolates subsets of variables providing significant discrimination as well as sltbsets of variables providing essentially as milch grollp separation as the original set of variables.

ISSN:0040-1706    

DOI:10.1080/00401706.1976.10489399

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

The problem is to estimate the number of points in and the size of a cluster when the points of the cluster are confounded with points having a smooth density (background or noise). The methods of estimation considered are maximum likelihood, minimumx2of the fit of counts in concentric annuli about the mean, and severalad hocprocedures. They are compared by application to computer simulated clusters where the density of the points in the clusters is assumed to be from a circularly symmetric bivariate distribution. The techniques are suitable for any system composed of individttal points, such as clusters of stars or galaxies, photometry of diffuse objects by digital image recorders, and measurement of energy or momentum of particles in a scattering experiment.

ISSN:0040-1706    

DOI:10.1080/00401706.1976.10489400

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

Two sequential procedures (one based on an initial group test) for reducing exposure to personnel leak-testing sealed radium sources where it is assumed that exposure is directly proportional to the activity of the source(s) being tested, were proposed in [19]. These procedures, based on finding at most one leaker, were evaluated and compared using a conditional binomial model—ne that assumed the presence of at most one leaker in the group being tested. Here the evaluation and comparison of the two procedures are based on a more realistic unconditional binomial model; in addition these two procedures are generalized to the case where at mostDleakers are searched for. The results obtained using both the conditional and unconditional models are compared.

ISSN:0040-1706    

DOI:10.1080/00401706.1976.10489401

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

In this article we introduce multiple stuttering-Poisson distributions and discuss their genesis, properties and applications. We consider a special case of triple stuttering-Poisson distribution with probability generating functionG(t) = Exp [a(t− 1) +b(t2− 1) +c(t3− l)] and investigate (1) maximum likelihood estimation, (2) moment estimation, and (3) mixed moment estimation of the parametersa,b,c. First order terms in the expressions for the biases and covariances of moment estimators are presented. The joint asymptotic efficiencies of moment estimators are tabulated for a few selected parameter points. The first order terms in the biases of maximum likelihood estimators and moment estimators are also given for a few selected parameter points. As judged from the contribution of the first order term, the possible bias of maximum likelihood estimators can be substantial over a considerable region of the parameter space. The moment estimators have low joint asymptotic efficiency over a large part of the parameter space. However, the moments of moment estimators are always finite. Estimation in four parameter distribution is also considered. An illustrative example is given and some concluding remarks concerning estimators are made.

ISSN:0040-1706    

DOI:10.1080/00401706.1976.10489402

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

Miilticollinesrity among the columns of regressor variables is known to cause severe distortion of the least squares estimates of the parameters in a multiple linear regression model. An alternate method of estimating the parameters which was proposed by the authors in a previous paper is Latent Root Regression Analysis. In this article several comparisons between the two methods of estimation are presented. The improvement of Latent Root Regression over ordinary least squares is shown to depend on the orientation of the parameter vector with respect to a vector defining the multicollinearity. Despite this dependence on orientation, the authors conclude that witch multicollinear data Latent Root, Regression Analysis is preferable to ordinary least squares for parameter estimation and variable selectJion.

ISSN:0040-1706    

DOI:10.1080/00401706.1976.10489403

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor