摘要:

The Π method for estimating an underlying smooth function ofMvariables, (xl, …,xm), using noisy data is based on approximating it by a sum of products of the form Πmφm(xm). The problem is then reduced to estimating the univariate functions in the products. A convergent algorithm is described. The method keeps tight control on the degrees of freedom used in the fit. Many examples are given. The quality of fit given by the Π method is excellent. Usually, only a few products are enough to fit even fairly complicated functions. The coding into products of univariate functions allows a relatively understandable interpretation of the multivariate fit.

ISSN:0040-1706    

DOI:10.1080/00401706.1991.10484799

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1991.10484800

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1991.10484801

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1991.10484802

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1991.10484803

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

Acomputational modelis a representation of some physical or other system of interest, first expressed mathematically and then implemented in the form of a computer program; it may be viewed as a function ofinputsthat, when evaluated, producesoutputs. Motivation for this article comes from computational models that are deterministic, complicated enough to make classical mathematical analysis impractical and that have a moderate-to-large number of inputs. The problem of designing computational experiments to determine which inputs have important effects on an output is considered. The proposed experimental plans are composed of individually randomized one-factor-at-a-time designs, and data analysis is based on the resulting random sample of observedelementary effects, those changes in an output due solely to changes in a particular input. Advantages of this approach include a lack of reliance on assumptions of relative sparsity of important inputs, monotonicity of outputs with respect to inputs, or adequacy of a low-order polynomial as an approximation to the computational model.

ISSN:0040-1706    

DOI:10.1080/00401706.1991.10484804

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

In accelerated life testing, information is sought about a process at normal stress levels by studying it at higher stress levels. Let Pr(t;x) be the probability of failure by timetof an item subjected to levelxof a stress. In this article, I consider the nonparametric proportional hazards model. Pr(t;x) = 1 –e−g(x)h(t), and the nonparametric accelerated failure time model, Pr(f;x) =F(g(x)t), where g andhare nonnegative nondecreasing functions ofxandt, respectively;Fis an arbitrary distribution function; and g has sigmoid (S-shaped) curvature. I develop confidence bounds for low-stress long-time probabilities and quantiles. I also discuss a goodness-of-fit test of the proportional hazards model. The results, which are primarily for data at two levels of stress, accommodate simple right censoring.

ISSN:0040-1706    

DOI:10.1080/00401706.1991.10484805

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

In the problem considered, a vector of many imprecise measurements (e.g., spectroscopic) is used to linearly predict a quantity whose precise measurement is difficult or expensive. The regression vector is estimated from a calibration experiment having both types of measurements for a random sample. Most previous approaches to this problem adjust for approximate multicollinearity, which often results from the correlations among the imprecise measurements, by inverting an approximation (e.g., factor-analytic) to their covariance matrix. In the approach here, it is argued that the regression vector should lie in a lower dimensional suhspace determined by the principal components of the covariance matrix. It is then estimated by applying a Stein contraction of the least squares estimator to the principal components regression estimator. Examples using real data are presented in which the proposed estimator substantially improves on the ordinary least squares estimation.

ISSN:0040-1706    

DOI:10.1080/00401706.1991.10484806

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

We consider estimation of quantiles and construction of prediction and tolerance intervals for a new response following a possibly nonlinear regression fit with transformation and/or weighting. We consider the case of normally distributed errors and, to a lesser extent, the nonparametric case in which the error distribution is unknown. Quantile estimation here follows standard theory, although we introduce a simple computational device for likelihood ratio testing and confidence intervals. Prediction and tolerance intervals are somewhat more difficult to obtain. We show that the effect of estimating parameters when constructing tolerance intervals can be expected to be greater than the effect in the prediction problem. Improved prediction and tolerance intervals are constructed based on resampling techniques. In the tolerance interval case, a simple analytical correction is introduced. We apply these methods to the prediction of automobile stopping distances and salmon production using, respectively, a heteroscedastic regression model and a transformation model.

ISSN:0040-1706    

DOI:10.1080/00401706.1991.10484807

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

Simultaneous calibration (or discrimination) intervals in regression were proposed by Lieberman, Miller, and Hamilton (1967) and by Scheffe (1973). Those procedures enable one to construct confidence intervals for the unobserved values of the independent variable corresponding to an unlimited sequence of observations of the dependent variable in a regression model. These calibration intervals are conservative in that they are obtained from simultaneous tolerance intervals for which the actual confidence level exceeds the nominal level. Furthermore, all other existing simultaneous tolerance intervals in regression are likewise conservative. In this article, we propose simultaneous tolerance intervals that are narrower than previous intervals. Given the tables of factors included in this article, they are also simple to construct and use in straightline calibration applications.

ISSN:0040-1706    

DOI:10.1080/00401706.1991.10484808

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor