摘要:

A review of the literature concerning experiments with mixtures is presented. Beginning with the work of Scheffe in 1958, the review covers approximately twenty papers in near chronological order, the last appearing in October 1971. Although priority in the treatment of designs for mixtures is claimed by Quenouille [27], and while others may argue that the work of Claringbold [6] was the impetus for Scheffé's research, the choice of starting with Scheffé is made because most of the authors of the reviewed papers recognized Scheffé as the person most instrumental in pioneering the work which has appeared over the past fourteen years.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489071

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489072

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

The instability of ordinary least squares estimates of linear regression coefficients is demonstrated for mortality rates regressed around various socioeconomic, weather and pollution variables. A ridge regression technique presented by Hoer1 and Kennard (Technometrics 12(1970) 69–82) is employed to arrive at “stable” regression coefficients which, in some instances, differ considerably from the ordinary least squares estimates. In addition, two methods of variable elimination are compared—one based on total squared error and the other on a ridge trace analysis.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489073

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

Several authors have considered point and interval estimation of the exponential scale parameter, σ, on the basis of subsets of the order statistics. In this paper, we suggest a procedure for finding approximate confidence intervals for σ in large samples, usingksample quantiles of a random sample of sizen. The procedure is based on a simple chi-square approximation to the distribution of the asymptotically best linear estimate of σ. We compare this procedure with the one given by Ogawa (1962) based on an approximatingt-distribution. We find that the interval based on the chi-square approximation is easier to calculate, and performs better whenkis small andnis large.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489074

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

The best linear unbiased estimator (BLUE), based onkselected sample quantiles from a large sample, of the scale parameter of the chi distribution with the degrees of freedom parameter,N, known is considered. The optimum spacings of the sample quantiles and the coefficients as well as the asymptotic relative efficiency of the BLUE are given fork= 1(1)6 andN= 1(1)30. WhenN> 30, a method to approximate the BLUE is given.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489075

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

Hoer1 and Kennard introduced a class of biased estimators (ridge estimators) for the parameters in an ill-conditioned linear model. In this paper the ridge estimators are viewed as a subclass of the class of linear transforms of the least squares estimator. An alternative class of estimators, labeled shrunken estimators is considered. It is shown that these estimators satisfy the admissibility condition proposed by Hoer1 and Kennard. In addition, both the ridge estimators and shrunken estimators are derived as minimum norm estimators in the class of linear transforms of the least squares estimators. The former minimizes the Euclidean norm and the latter minimizes the design dependent norm. The class of estimators which are minimum variance linear transforms of the least squares estimator is obtained and the members of this class are shown to be stochastically shrunken estimators. An example is computed to show the behavior of the different estimators.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489076

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

In fitting partially linear statistical models by least squares, several authors have demonstrated that, for fixed values of the nonlinear parameters, optimum values of the linear parameters can be determined analytically. Thus, the linear parameters can be eliminated by substitution. This reduction in the problem's dimension seems to greatly facilitate its solution by nonlinear least squares algorithms. In many applications, the partially linear model includes a strictly linear portion. In the present article, it is shown that for such models a considerable further reduction can be obtained in the necessary computations. Simultaneously, the earlier results are extended to a much broader class of models and to weighted least squares, and full-rank assumptions are removed. Under certain conditions that are generally satisfied in practice, the reduced model and sum of squares, considered as functions of the nonlinear parameters, have partial derivatives. Analytical expressions for these partials are obtained.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489077

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

Techniques for the analysis of mixture data are discussed. It is shown that mixture models often can be simplified by observing near equalities among the estimated coefficients. Expressing the components in terms of pseudocomponents will sometimes improve the fit of Becker's models [1] and improve the numerical analysis. Scatter plots are useful in detecting dominant components in a mixture system. The ratio model is shown to be a useful alternative to the polynomial and Becker's models. Examples are presented to illustrate these methods of analysis.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489078

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

In this paper, the reliability of a system withNindependent components supplied with a pool ofsspares is investigated. The components have an exponential life time distribution and the failed components are repaired, one at a time, with a general repair time distribution. Numerical results are presented for the mean time to system failure (system is said to fail when a component fails with no spare available) and the reliability of the system in some special cases of interest.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489079

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

A simple, unbiased estimator, based on a censored sample, has been proposed by Rain [1] for the scale parameter of the Extreme-value distribution. This estimator was shown to have high efficiency and to be approximately distributed as a chi-square variable if substantial censoring occurs. Further small sample and asymptotic properties of this estimator are considered in this paper. The estimator is modified so that it is more applicable to the complete sample case and a close chi-square approximation is established for all cases. The estimator is also shown to be related to the maximum likelihood estimator.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489080

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor