摘要:

The user of RSM techniques gains considerable insight into the nature of the stationary point and the nature of the underlying response surface from estimates of the eigenvalues of the matrix of pure and mixed quadratic regression coefftcients,B. This article presents and illustrates methodology for constructing conservative confidence limits on the eigenvalues of this matrix as well as the mean response at a constrained optimum. When a confidence interval about an eigenvalue ofBincludes zero, a change in the strategy of analysis is required; one is suggested and illustrated.

ISSN:0040-1706    

DOI:10.1080/00401706.1986.10488152

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

In this article exact tests for the equality of parameters from several correlated linear response models with an unknown variance–covariance matrix Σ are presented. The models are assumed to be of the same form and to contain the same set of input variables. The development of the proposed tests is based on a multivariate representation of the system of response models as a single linear multiresponse model. Comparisons among the models' parameter vectors can then be formulated as a general linear hypothesis under the multiresponse model. Any of the commonly used multivariate test statistics—Roy's largest root, Wilks's likelihood ratio, Hotelling–Lawley's trace, or Pillai's trace—can be used subsequently to test this hypothesis. An investigation is made with regard to the effects of design multicollinearity and structure of the variance–covariance matrix Σ on the power of the multivariate tests. A numerical example involving three response models and two input variables is used to illustrate the application of the multivariate tests.

ISSN:0040-1706    

DOI:10.1080/00401706.1986.10488153

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The nonparametric maximum likelihood estimate (NPMLE) of a distribution functionG, based on a random sample fromG, under the assumption thatGhas a monotone decreasing densityg, is the least concave majorant of the empirical distribution function (Barlow, Bartholomew, Bremner, and Brunk 1972). This may lead one to believe that the least concave majorant of the Kaplan-Meier (1958) estimate is the NPMLE ofGin the “arbitrary right censorship model”—that is, when the data include right censored observations and no assumption on the censoring mechanism is made. This, however, is not correct, as was pointed out by McNichols and Padgett (1982), and the problem of fully characterizing the solution to this problem has been left open, In this article we provide such a characterization in two steps. First, we show that when the largest observation is censored the NPMLE ofGis not a proper distribution (the nonparametric likelihood function has a supremum but not a maximum). This suggests that as a numeric tool one should restrict the maximization problem to distributions with finite support—say, [0,M] for some very largeM. Second, we describe an iterative scheme with an extremely simple iteration step, which is guaranteed to converge monotonically (in the sense of increased likelihood in each step) to the NPMLE ofGon [0,M]. Unlike the Kaplan-Meier estimate, for which the associated density estimate places mass at a discrete set of points, the method in this article produces directly a proper estimate of the densityg. Of course, the method can also be used with uncensored data, in which case it produces the least concave majorant of the empirical distribution function.

ISSN:0040-1706    

DOI:10.1080/00401706.1986.10488154

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

This study compared three biased estimation and four subset selection regression techniques to least squares in a large-scale simulation. The parameters relevant to a comparison of the techniques involved were systematically varied over wide ranges. A parameter of importance not used in previous major simulations of subset techniques, the proportion of independent variables in the data that were superfluous, was included. The major result is that neither biased estimation nor subset selection demonstrated a consistent superiority over the other, excluding stepwise and principal component regression, both of which performed poorly.

ISSN:0040-1706    

DOI:10.1080/00401706.1986.10488155

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Techniques are developed for the change-point problem when the data are a series of correlated normal variables, combining locally most powerful testing with Bayesian estimation. The approach is applied to a nuclear materials accounting problem. The effect of correlation on change-point tests is examined.

ISSN:0040-1706    

DOI:10.1080/00401706.1986.10488156

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Some directional data collected in a system evaluation of illumination flares are presented. Preliminary analysis suggested a need for procedures to detect, estimate, and test the significance of possible change points in the data. In this article some nonparametric procedures are proposed and applied to the data.

ISSN:0040-1706    

DOI:10.1080/00401706.1986.10488157

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1986.10488158

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1986.10488160

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1986.10488162

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1986.10488165

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor