摘要:

This paper deals with some of the statistical properties of, and methods of analysis for, conventional residuals from additivity in two-way tables. Attention is given to three cases: (i) normal fluctuations superimposed on an additive model; (ii) one outlier added to the condition described in (i); and (iii) two outliers superimposed on the condition in (i). The results are based mainly on empirical sampling and involve average values, correlation properties, the use of theW-statistic (Shapiro and Wilk [24]) and of probability plotting methods. Generally speaking, in the null case of no outliers, the residuals do behave much like a normal sample. When one outlier is present, the direct statistical treatment of residuals provides a complete basis for data-analytic judgments, especially through judicious use of probability plots. When two outliers are present, however, the resulting residuals will often not have any noticeable statistical peculiarities.

ISSN:0040-1706    

DOI:10.1080/00401706.1975.10489265

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

After stating the model and the design problem, we briefly present the results for regression design prior to the work of Kiefer and Wolfowitz. We then review the major results of Kiefer and Wolfowitz, particularly those on the theory of design, as well as the way the criterion has been extended to non-linear models. Finally, we discuss algorithms for constructingD-optimum designs.

ISSN:0040-1706    

DOI:10.1080/00401706.1975.10489266

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

Designs are suggested for estimating the restricted parameters in Cox's mixture polynomial. The variances of the restricted estimates of the parameters are minimum when using the simplex-lattice designs suggested by Scheffé The precision of the estimates, in terms of their variances, as affected by the location of the design points as well as the locationofthe standard mixturesis also discussed. It is shown for the vertex design centered atsthat ifsis positioned on the axis of an individual component, the closerslies to the vertex of the simplex representing the individual component, the more precise will be the parameter estimates associated with the individual component relative to the other components. A numerical example is presented to illustrate the difference in the interpretations given to the parameter estimates associated with the Cox polynomial and the Scheffé polynomial.

ISSN:0040-1706    

DOI:10.1080/00401706.1975.10489267

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

The problem of selecting a design and estimating procedure for estimating with minimum mean squared error (MSE) the variance components in a two-stage nested random model is considered. For balanced designs a modified maximum likelihood (ML) estimator is superior, and for this estimator the optimal design is less sensitive to the intra-class correlation τ for τ ≤ .5 than those designs based on minimizing the variance of the usual analysis of variance (AOV) estimator. For τ > .5, where an unbalanced design is preferable, asymptotic results were derived to indicate optimal designs for ML and AOV estimators; ML estimators have smaller MSE's than truncated AOV estimators or iterated least squares estimators. The optimal number of classes is somewhat less than the number needed for minimizing the variance of the usual AOV estimator. Large sample results for unbalanced designs were compared with small sample results obtained by simulation for a wide range of intra-class correlation and several selected designs.

ISSN:0040-1706    

DOI:10.1080/00401706.1975.10489268

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

The Nelder-Mead simplex method for function minimization is a “direct” method requiring no derivatives. The objective function is evaluated at the vertices of a simplex, and movement is away from the poorest value. The process is adaptive, causing the simplexes to be continually revised to best conform to the nature of the response surface. The generality of the method is illust'rated by using it. to solve six problems appearing in the May 1973 issue ofTechnometrics.

ISSN:0040-1706    

DOI:10.1080/00401706.1975.10489269

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

Duplicate measurements are used routinely in the chemical laboratory as a check on the results. In case of disagreement, a third measurement is taken. There are a number of possible ways in which the third observation can be used. This paper discusses several commonly used procedures, together with their impact on the estimation of the mean. It is shown that. in the presence of outliers, the mean of the closest pair is a better estimator of the mean than either the median or the remaining observation.

ISSN:0040-1706    

DOI:10.1080/00401706.1975.10489270

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

An approximate solution for comparing the means of two populations when the ratio of the variances is unknown has been developed by Welch. This method is adapted to the problem of calculating confidence intervals for sums of regression–based estimates, where each estimate in the sum comes from a different regression equation. The formulas for calculating the approximation are presented. An example is also presented to ilustrate the use of the approximation.

ISSN:0040-1706    

DOI:10.1080/00401706.1975.10489271

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

We consider tests based on one observation on each ofN≥ 2 random variablesXl, …,XNto decide if the means μ of thexi's are all equal against the one-sided alternative that a shift has occurred at some unknown point γ, (i.e. μ1, = μ2= … = μr< μr+1= … = μN). Thexi's are considered to be normally distributed with a common unknown variance. Bayesian tests as well as a test based on the maximum likelihood estimate of γ are considered and their powers are compared by Monte Carlo methods. The exact distribution of a Bayesian test statistic is derived. A simple application using traffic accident data is presented.

ISSN:0040-1706    

DOI:10.1080/00401706.1975.10489272

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

An approximation to the average run length for cumulative sum control charts is derived using the analogy between this procedure and the sequential probability ratio test for normal observations. This approximation is also derived by using a Brownian motion approximation to the cumulative sum. The Brownian motion approximation does not require the normality assumption. The analytical expression for the average run length obtained from the approximation is then used to determine the optimal choice of parameters to minimize the average run length at a specified deviation flom control, subject to a fixed average run length when in control.

ISSN:0040-1706    

DOI:10.1080/00401706.1975.10489273

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

We continue the study by developing another approximation to the cumrdative sums which allows one to study the run length distribution after a change in level occurred. This approximate distribution is doubly important because it also applies to the situation of stable operation when the reference value is such that the terms of the sum have a non-zero mean. The major emphasis here is on the effects on the run length distribution caused by the presence of serial correlation. The approximation introduced holds for first order moving average models and first order autoregressive models and particular attention is paid to these error structures. A Monte Carlo study with normal observations is used to check the accuracy of the approximations. The presence of serial correlation is seen to have quite a major influence on the run length distribution.

ISSN:0040-1706    

DOI:10.1080/00401706.1975.10489274

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor