摘要:

If we assume no higher order interactions for the 2n3mfactorial series of designs, then relaxing the restrictions concerning equal frequency for the factors and complete orthogonality for each estimate permits considerable savings in the number of runs required to estimate all the main effects and two-factor interactions. Three construction techniques are discussed which yield designs providing orthogonal estimates of all the main effects and allowing estimation of all the two-factor interactions. These techniques are: (i) collapsing of factors in symmetrical fractionated 3m–pdesigns, (ii) conjoining fractionated designs, and (iii) combinations of (i) and (ii). Collapsing factors in a design either maintains or increases the resolution of the original design, but does not decrease it. Plans are presented for certain values of (n, m) as examples of the construction techniques. Systematic methods of analysis are also discussed.

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490735

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

A parsimonious stepwise procedure for obtaining least squares solutions of multiple regression eqllntions when the regression coefficients are subject to arbitrary but consistent linear restraints is presented. The method is also applicable to the minimization of positive definite quadratic functions. Key to the method is the use of the elements of the appropriate inverse matrix for determining the standardized distance from any unrestricted, or conditionally unrestricted, solution to any boundary or boundary intersection of the permissible region for the regression coefficients.

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490736

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

A method of adaptive nonparametric classification based on counting known points “observed” within a hypersphere inserted in the character space is described. It is shown that an optimal single-hypersphere decision process exists, and that the proposed procedure converges stochastically to the optimal process. The latt)er in turn convrrges at maximum rate to the likelihood ratio decision rule. Sampling experiments on multivariate normal populations indicate that the efficiency of the method when the parametric model holds is about the same as that of the standard parametric procedure.

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490737

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490738

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

A test based on maximum likelihood estimators is given for testing the equality of the shape parameters in two Weibull distributions with the scale parameters unknown. Tests for the equality of the scale parameters are also presented along with a procedure for selecting the Weibull process with the larger mean life.

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490739

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

An algorithm involving polynomial approximations for evaluation of the normal distribution function is presented which may be implemented in fast and accurate computer programs of moderate length. Using this approximation and simple two-step Newton-Raphson iteration, the evaluation of the inverse normal distribution function is achieved with reasonable accuracy.

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490740

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

It is emphasized that the singular decomposition of a matrix has a variety of uses, especially in statistics, although it is seldom mentioned in books on either matrices or statistics. Some applications are surveyed and some new ones are given.

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490741

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490742

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490743

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1969.10490745

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor