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21.
Several extensions of the popular E(s 2) criterion of Booth and Cox (1962) to multilevel supersaturated designs have been advanced in literature. These extensions are not unique due to different ways they measure overall nonorthogonality between all pairs of the columns of the model matrix. We exploit the connection of the E(s 2) criterion with A- and D-optimality that naturally lends itself to a generalized criterion for the multilevel situation in a unified way. The extensions provided in literature follow as special cases of the generalized criterion. A lower bound to the generalized criterion is derived for a wide class of designs, and a method of construction for the symmetrical case is discussed. 相似文献
22.
Philip Prescott 《统计学通讯:理论与方法》2013,42(5):763-784
In practical situations involving mixtures formed from several ingredients, interest is sometimes centered on the response in an ellipsoidal neighborhood around a standard formulation. We show that standard, orthogonally blocked, response surface designs, defined on a q ? 1 dimensional unit sphere, may be transformed into similarly orthogonally blocked q-ingredient mixture designs defined within an ellipsoid centered at the standard formulation. The method is illustrated using several examples of mixture experiments with three, four, and five ingredients, arranged in two, three, or four orthogonal blocks, obtained by projecting standard central composite designs and Box–Behnken designs into the ellipsoidal mixture region. Rotations of the resulting designs within the ellipsoidal regions are also considered. 相似文献
23.
Consider the problem of testing the isotonic of several p-variate normal mean vectors against all alternatives. It is difficult to compute the exact p-value for this problem of testing with the classical method when the covariance matrices are completely unknown. In the present paper, a test statistic is proposed for this problem of testing. A reformulation of the test statistic is given based on the orthogonal projections on the closed convex cones and then the upper bound for p-value of the test statistic is computed. 相似文献
24.
A new method of construction of orthogonal resolution IV designs for symmetrical and asymmetrical factorials has been presented. Many new series of orthogonal factorial designs of resolution IV can be obtained by the above general method. 相似文献
25.
For two-level factorials, we consider designs in N=2 (mod 4) runs as obtained by adding two runs, with a certain coincidence pattern, to an orthogonal array of strength two. These designs are known to be optimal main effect plans in a very broad sense in the absence of interactions. Among them, we explore the ones having minimum aberration, with a view to ensuring maximum model robustness even when interactions are possibly present. This is done by sequentially minimizing a measure of the bias caused by interactions of successively higher orders. 相似文献
26.
T. Imada 《统计学通讯:模拟与计算》2013,42(6):894-906
Assuming that all components of a normal mean vector are simultaneously non negative or non positive, we consider a multivariate two-sided test for testing whether the normal mean vector is equal to zero or not. Since the likelihood ratio test is accompanied with theoretical and computational complications, we discuss two kinds of approximations of the likelihood ratio test. One is based on a conservative critical value determined by a certain inequality. The other is constructed by the approximation of the likelihood ratio test proposed by Tang et al. (1989). We compare the likelihood ratio test and two kinds of approximations through numerical examples regarding critical values and the power of the test. 相似文献
27.
Brian J. McCartin 《Statistics》2013,47(3):187-206
The geometric characterization of linear regression in terms of the ‘concentration ellipse’ by Galton [Galton, F., 1886, Family likeness in stature (with Appendix by Dickson, J.D.H.). Proceedings of the Royal Society of London, 40, 42–73.] and Pearson [Pearson, K., 1901, On lines and planes of closest fit to systems of points in space. Philosophical Magazine, 2, 559–572.] was extended to the case of unequal variances of the presumably uncorrelated errors in the experimental data [McCartin, B.J., 2003, A geometric characterization of linear regression. Statistics, 37(2), 101–117.]. In this paper, this geometric characterization is further extended to planar (and also linear) regression in three dimensions where a beautiful interpretation in terms of the concentration ellipsoid is developed. 相似文献
28.
K. ChatterjeeC. Koukouvinos K. Mylona 《Journal of statistical planning and inference》2011,141(2):877-888
In this paper, a new lower bound to A2-optimality measure is derived and is applied to multi-level and mixed-level column balanced designs. A2-optimal multi-level and mixed-level designs are obtained by the application of the new lower bound. 相似文献
29.
In this paper, we propose a new nonparametric simultaneous test for dual alternatives. Simultaneous tests for dual alternatives are used for pattern detection of arsenic contamination level in ground water. We consider two possible patterns, namely, monotone shift and an umbrella-type location alternative, as the dual alternatives. Pattern recognition problems of this nature are addressed in Bandyopadhyay et al. [5], stretching the idea of multiple hypotheses tests as in Benjamini and Hochberg [6]. In the present context, we develop an alternative approach based on contrasts that helps us to detect three underlying pattern much more efficiently. We illustrate the new methodology through a motivating example related to highly sensitive issue of arsenic contamination in ground water. We provide some Monte-Carlo studies related to the proposed technique and give a comparative study between different detection procedures. We also obtain some related asymptotic results. 相似文献
30.