摘要:

We introduce a pair of displays that summarize the behavior of the regression coefficients and the corresponding residuals, that are obtained when the “trimming” parameter in Huber's family ofM-estimates is allowed to vary continuously over its whole range [0, ∞], The displays exhibit the degree to which the estimates and residuals are sensitive to changes in the implicit weights attached to the worst-fitting points. They are thus effective in identifying the presence and influences of any outliers that occur in the data. They can also be used to select a single “best” set of estimates and the associated residuals.

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489492

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

A new measure based on confidence ellipsoids is developed for judging the contribution of each data point to the determination of the least squares estimate of the parameter vector in full rank linear regression models. It is shown that the measure combines information from the studentized residuals and the variances of the residuals and predicted values. Two examples are presented.

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489493

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

Simple estimators of the parameters σ, β and σ of the simple linear regression model, based upon trimmed samples, and called adjusted Trimmed Estimators (ATE) are introduced. They are very easy to compute, and their coefficients may be chosen so that their efficiency relative to the (O-BLUE) from complete samples is equal to one. The coefficients are given for five symmetric distributions, namely, the normal distribution, the scale contaminated normal distributions with a scale factor of σ = 3.0 and contamination proportions ∊ = 0.01, .05 and .1O and the double exponential distribution, for values of 5 ≤n≤ 20 and different amounts of trimming (g). The estimators are shown to be biased, but the exact amounts of bias are given. Adjusted Efficiency Robust Estimators (AERE) are also introduced. They are shown to maintain high efficiency relative to the (O-BLUE) under changes in the distribution of the errors.

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489494

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

A simple generalization of the usual ridge regression estimator for the linear regression model is given which avoids the need to center all variables. The estimator is proved to be location invariant. This estimator is of pedagogical interest and in forecasting also of practical importance.

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489495

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

The published mixture models are briefly recapitulated and a type of model which combines Scheffé polynomials and inverse terms is suggested. This model is applied to an example of published data and found to be a potentially useful one.

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489496

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

Extreme vertices designs were developed by McLean and Anderson [9] for situations where components are restricted by lower and upper bounds. We give here a transformation which provides alternative designs, construcked through symmetric-simplex designs [10], for restricted exploration. These designs can provide uniform exploration of the restricted factor-space (polyhedron) and avoid clusters of points.

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489497

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

Consider two treatments and a combination of them. Givennavailable experimental units, the problem is to determine the number of unitsn, to be assigned to the first treatment,n2to the second, andn, to the combination,n= Σi,ni,ni≥ 0,i= 1, 2, 3, subject to suitable optimality criteria. This study was motivated by an example of a weighing design withn= 18.n1= 2.n2= 9,ns= 7 given by Box and Tiao [2, Section 2.7.3]. The allocation seemed far from optimal leading to the present investigation.

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489498

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

Multinomial samples may be fully or partially classified. In this paper, procedures for optimally determining sample size allocations between fully and partially classified data sets are described and illustrated. Expressions for the large-sample variances of the maximum likeli-hood estimators using both completely and partially classified data are given which reduce the design problems to convex programming problems.

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489499

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

A solution is given to the problem of using a variable correlated with a performance variable to screen a product when the correlation is unknown or when the proportion of presently acceptable product is unknown. The procedure involves setting lower confidence limits on these unknown parameters and then relating the confidence coefficient to the probability of the procedure attaining a required proportion of acceptable product. The performance variable and screening variable are assumed to be jointly normally distributed.

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489500

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

Exponential, Weibull, gamma and log-normal models are frequently used in the analysis of failure time data. By extending the generalized gamma model of Stacy [l5]. Prentice [13] showed that the models listed are all embraced by a single parametric family. Likelihood methods were described for discrimination among the special cases and for assessment of each within the more comprehensive framework. Here, such methods are applied to several recent data sets from the industrial and medical literature in order to study distributional shape. New results are given for the accommodation of censoring and regression variables. The appropriateness of Weibull and lognormal models is emphasized.

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489501

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor