A simpler way of obtaining non-sIngularity conditions of rotatability

In response surface designs, it is not usually easy to handle the moment matrix X'X, especially for higher orders. This paper presents a method in which the moment matrix of a response surface of any order can be standardized, i.e., X'X splits into a diagonal matrix consisting of sub-matrices of lower order. This eases the calculation of the determinant and the inverse of X'X. The method has been illustrated with applications to second, third and fourth order response surfaces.     

A note on connectedness in fixed effects manova and gmanova models withmissing cells

Murray and Smith (1985) and Hocking (1985) give a generalized definition and test of connectedness in the case of missing cells using the univariate cell-means model with linear restrictions on the cell-means. The test of connectedness is here extended to multivariate fixed effects models, including the usual MANOVA model with linear restrictions, the MANOVA model with double linear restrictions, and the GMANOVA model.     

On the robustness of the extreme deviate test for a single multivariate outlier against heavy-tailed distributions

In this paper we assess the sensitivity of the multivariate extreme deviate test for a single multivariate outlier to non-normality in the form of heavy tails. We find that the empirical significance levels can be markedly affected by even modest departures from multivariate normality. The effects are particularly severe when the sample size is large relative to the dimension. Finally, by way of example we demonstrate that certain graphical techniques may prove useful in identifying the source of rejection for the multivariate extreme deviate test.     

The two-sample t test versus satterthwaite's approximate f test

A comparison between the two-sample t test and Satterthwaite's approximate F test is made, assuming the choice between these two tests is based on a preliminary test on the variances. Exact formulas for the sizes and powers of the tests are derived. Sizes and powers are then calculated and compared for several situations.     

Testing a main effect in a three factor mixed model

In the present paper, the author has considered and compared the power of three test procedures, based on two preliminary tests of significance (PTS), for testing a main effect in a three factor factorial experiment. Davenport and Webster (1973) type test statistics are used in the final test. Recommendation for a suitable size of PTS has been made so that the power of a test procedure is adequately high.     

Estimators based on ranks for arma models

In this paper we introduce a new family of robust estimators for ARMA models. These estimators are defined by replacing the residual sample autocovariances in the least squares equations by autocovariances based on ranks. The asymptotic normality of the proposed estimators is provided. The efficiency and robustness properties of these estimators are studied. An adequate choice of the score functions gives estimators which have high efficiency under normality and robustness in the presence of outliers. The score functions can also be chosen so that the resulting estimators are asymptotically as efficient as the maximum likelihood estimators for a given distribution.     

The graphical advantages of finite interval confidence band procedures

When presented as graphical illustrations, regression surface confidence bands for linear statistical models quickly convey detailed information about analysis results. A taut confidence band is a compact set of curves which are estimation candidates for the unobservable, fixed regression curve. The bounds of the band are usually plotted with the estimated regression curve and may be overlaid by a scatter-plot of the data to provide an integrated visual impression. Finite-interval confidence bands offer the advantages of clearer interpretation and improved efficiency and avoid visual ambiguities inherent to infinite-interval bands. The definitive characteristic of a finite-interval confidence band is that it is only necessary to plot it over a finite interval in order to visually communicate all its information. In contrast, visual representations of infinite-interval bands are not fully informative and can be misleading. When an infinite-interval band is plotted, and therefore truncated, substantial information given by its asymptotic behavior is lost. Many curves that are clearly within the plotted portion of the infinite interval confidence band eventually cross a boundary. In practice, a finite-interval band can always be easily obtained from any infinite-interval band. This article focuses on interpretational considerations of symmetric confidence bands as graphical devices.     

Testing non-oblique hypotheses

This paper considers a likelihood ratio test for testing hypotheses defined by non-oblique closed convex cones, satisfying the so called iteration projection property, in a set of k normal means. We obtain the critical values of the test using the Chi-Bar-Squared distribution. The obtuse cones are introduced as a particular class of cones which are non-oblique with every one of their faces. Examples with the simple tree order cone and the total order cone are given to illustrate the results.     

Heine-euler extensions of the poisson distribution

The paper shows that the Heine and Euler distributions (Benkherouf and Bather, 1988) are members of a family of q-series anologues of the Poisson distribution, with similar probability mass functions, but different restrictions on their parameters, and different modes of genesis and properties. The relationships between the Heine, Euler, pseudo-Euler, Poisson and geometric distributions are explored. Illustrative data sets are discussed.     

Shape properties of the g-and-h and johnson families

A substantial part of examining the properties of a distributional family consists of considering shape properties. It is important that this examination is sufficiently thorough to enable understanding of the behaviour of the family, its comparison with others, and to assist in developing future families. The g-and-h distributions and the Johnson system are examined here in these terms