摘要:

A method, based upon minimizing estimators of the criteriaE(L12) andE(L22), is given for selecting thek1, in generalized ridge regression; an explicit, closed form solution is developed for the resulting estimator β* of the vector of parameters,β, in the linear regression model. A method is also proposed for obtaining constrained generalized ridge estimators, with constraints placed upon β*, to utilize a priori information concerning the signs of the model parameters along with ridge estimation. These and other ridge estimation procedures are then examined and compared with least squares or constrained least squares estimators in a Monte Carlo study which demonstrates their effectiveness. An example is given to indicate their behavior and use on an applied problem.

ISSN:0040-1706    

DOI:10.1080/00401706.1978.10489634

出版商:Taylor & Francis Group    

年代:1978

数据来源: Taylor

摘要:

In this paper we examine the relationship between the general ridge estimator and the standardized ridge estimator.

ISSN:0040-1706    

DOI:10.1080/00401706.1978.10489635

出版商:Taylor & Francis Group    

年代:1978

数据来源: Taylor

摘要:

A jack knife procedure for constructing confidence regions in nonlinear regression is examined using Monte Carlo simulation. The jack knife promises to be asymptotically double-edged, being both independent of linearizing approximations to the regression surface and insensitive to specification of the error distribution. For moderate sample sizes the jack knife cannot be trusted in establishing joint confidence regions.

ISSN:0040-1706    

DOI:10.1080/00401706.1978.10489636

出版商:Taylor & Francis Group    

年代:1978

数据来源: Taylor

摘要:

A framework, called α-acceptability, is proposed for evaluating alternatives to the usual least squares estimates of regression coefficients. An estimate is defined to be α-acceptable if it is in the usual (1 - α) 100% confidence region, Estimates which are α-acceptable for large values of α, such as .99 (corresponding to a 1% confidence region) are viewed as statistically indistinguishable from the usual estimates and, in a sense, simply rounded off. Applications to subset selection, ridge regression, and a class of minimax procedures are discussed and illustrated with an example.

ISSN:0040-1706    

DOI:10.1080/00401706.1978.10489637

出版商:Taylor & Francis Group    

年代:1978

数据来源: Taylor

摘要:

This paper deals with the problem of constructing a confidence band over the real line for a polynomial regression curve of known degree. The situation involves successive, and therefore in general, correlated measurements, say, in time, on the same objects. Two methods for constructing these bands are developed when the measurements are assumed to be multivariate normal. They are then compared to determine when one provides narrower bandwidths than the other. The confidence level I – α is, in general, a lower bound.

ISSN:0040-1706    

DOI:10.1080/00401706.1978.10489638

出版商:Taylor & Francis Group    

年代:1978

数据来源: Taylor

摘要:

In many applications a response variable,y, may not be adequately represented by a polynomial function of the input variable,x, over the entire experimental space. Often a desirable choice of a regression model is one which consists of grafted polynomial submodels.

ISSN:0040-1706    

DOI:10.1080/00401706.1978.10489639

出版商:Taylor & Francis Group    

年代:1978

数据来源: Taylor

摘要:

A new balanced incomplete block design forv= |8,b= 5|,r= 17,k= 6. λ = 5 is presented. The design is resolvable and can be split into useful partially balanced suhdesigns. When these designs are used for the 2 × 32factorial experiment they all have factorial structure.

ISSN:0040-1706    

DOI:10.1080/00401706.1978.10489640

出版商:Taylor & Francis Group    

年代:1978

数据来源: Taylor

摘要:

In this paper several designs featuring planned unbalance are compared, using maximum likelihood (ML), for the estimation of variance components in a two-way classilicatlon model with no interaction. Asymptotic and small sample results are presented. A transformation technique is discussed for simplifying the variance-covariance matrix thereby improving the efficiency of the asymptotic computing routines and rendering the small sample simulation procedures computationally feasible. Evidence is offered in support of the viewpoint that asymptotic findings are consistent with small sample ML results for design selection if the relative asymptotic results for comparing two designs are not too close to one.

ISSN:0040-1706    

DOI:10.1080/00401706.1978.10489641

出版商:Taylor & Francis Group    

年代:1978

数据来源: Taylor

摘要:

Exact prediction intervals, based upon maximum likelihood estimation, for thekth future observation of a Weibull process are derived. Fork= 1, an exact, closed-form prediction limit is given. Fork> 1, the exact solution, and a simpler approximate prediction limit are both given.

ISSN:0040-1706    

DOI:10.1080/00401706.1978.10489642

出版商:Taylor & Francis Group    

年代:1978

数据来源: Taylor

摘要:

This paper presents maximum likelihood theory for large-sample optimum accelerated life test plans. The plans are used to estimate a simple linear relationship between (transformed) stress and product life, which has a Weibull or smallest extreme value distribution. Censored data are to be analyzed before all test units fail. The plans show that all test units need not run to failure and that more units should be tested at low test stresses than at high ones. The plans are illustrated with a voltage-accelerated life test of an electrical insulating fluid.

ISSN:0040-1706    

DOI:10.1080/00401706.1978.10489643

出版商:Taylor & Francis Group    

年代:1978

数据来源: Taylor