摘要:

A new method for determining least squares estimators for certain classes of non- linear models is discussed. The method is an extension of a variable projection method of Scolnik (1970), and involves the minimization of a modified functional. The feature of minimizing this modified functional is that for a certain class of non-linear models, called the constant-coefficients case, only one half the parameters are involved initially. To find the estimators of the remaining parameters is straight forward and relatively easy. This new two step-procedure is shown to be equivalent to the over-all least squares procedure. We also discuss the case of a class of models called the variable coefficients class. For this case, we formulate a new algorithm for determining the estimators which makes use of approximate confidence regions for the parameters.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489035

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

This paper discusses various spectral windows which can be used to estimate spectra and cross-spectra. Suggestions are offered which may be helpful in choosing a window for a particular application. The results of the prediction technique are compared with the results of standard regression analysis on several examples. Criteria are given for choosing between these two approaches to nonlinear prediction.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489036

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

The estimation of parameters in nonlinear algebraic models is considered for a general class of problems. Included are problems where both the independent and dependent variables are subject to error and problems where the model is algebraically implicit. The maximum likelihood principle leads to an equality constrained minimization problem. An algorithm to achieve this minimization is obtained through the use of Lagrange multipliers.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489037

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

A procedure with exact frequency, Bayesian and fiducial interpretation is given for the problem indicated in the title. Some discussion, which applies with minor changes to other problems of location and scale, is given of the relationship betweeen these three approaches.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489039

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

In studying the waiting times between failures of a series system whose components fail independently and are replaced upon failure, it is well known that for large systems in time equilibrium, the distribution of waiting times is approximately exponential. Correction terms are available to account for the finite number of components. Here, correction terms are developed for the finite age of the system as well. Also numerical studies are presented indicating the magnitude of the error in reliability predictions based on the assumption of time equilibrium when system age is really finite.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489040

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

In Boardman and Kendell (1970a) m.l. estimation of the parameters from right censored, compound exponentials was considered when the exact failure times were known. In the present paper approximate m.l. estimates are obtained when the data are collected only atkspecified time intervals. The properties of an initial estimator are studied and shown to compare very favorably with those found above. A numerical example is considered to illustrate the use of the grouped estimators.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489041

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

Jaech [2] considers point and interval estimation of the shape parameter in the Weibull distribution based on two failures per lot from one or more lots. This paper provides similar procedures for two or more failures per lot. Point estimation procedures for the scale parameter and for reliability are also provided, and interval estimation is considered for the two failures per lot case. Some comparisons of the estimators with maximum likelihood estimators and a comparison of the relative expected experiment time for censored sampling compared to complete sampling are also included.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489042

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

The scale parameter of an exponential distribution is reparameterized as a function of the stress according to the Arrhenius Re-action Rate Model. The location parameter is reparameterized as a linear function of the stress. Maximum likelihood estimators of the parameters of the Arrhenius model and the weighted least squares estimators of the linear model are obtained using data from censored sample accelerated life tests. The asymptotic normality of the maximum likelihood estimators is ascertained by examining the shapes of their maximum relative likelihood functions. The asymptotic normality of the least squares estimators is ascertained by establishing certain criteria for convergence. An unbiased estimator for the mean life of the device at use condition stress μuis obtained. Confidence limits for μu, are difficult to obtain, and alternatively a plausibility interval for μuis obtained.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489043

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

The purpose of this paper is to present the theory and develop an algorithm associated with the exploration of a dual response surface system. The approach is to find conditions on a set of independent or “design” variables which maximize (or minimize) a “primary response” function subject to the condition that a “constraint response” function takes on some specified or desirable value. A method is outlined whereby a user can generate simple two dimensional plots to determine the conditions of constrained maximum primary response regardless of the number of independent variables in the system. He thus is able to reduce to simple plotting the complex task of exploring the dual response system. The procedure that is used to generate the plots depends on the nature of the individual univariate response functions.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489044

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

For the second order estimating function, ŷ(x), and third order true function η(x) in two variables, secondary criteria are used to select a design from the class of average minimum bias designs. It is shown that designs can be constructed which not only allow estimation of a cubic model with nearly minimum variance averaged over a square but also provide for efficient lack of fit tests. Average qiradratic variance is also evaluated. Specific 12 point and 16 point designs are recommended.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489045

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor