证明H≤G≤X的捷径

证明Ｈ≤Ｇ≤Ｘ的捷径江西财经学院程振源算术平均数、调和平均数和几何平均数存在如下数量关系：Ｈ≤Ｇ≤Ｘ。不少统计学教材指出了它们间的这种数量关系，但都未曾予以证明。项威同志在《三种平均数的数量关系》一文中提供了一种证明方法（见《中国统计》１９９４年第２...     

2m fractional factorial designs of resolution V with high A-efficiency, 7 ⩽ m ⩽ 10

We present 111 2^m fractional factorial designs of resolution V for 7 ⩽ m ⩽ 10. These designs are the best known to the authors with respect to the A-optimality criterion (as of October 1995).     

Percentage points of the joint distribution of the extreme roots of the random matrix S1(S1+S2)−1

The numerical treatment of nonlinear model fitting problems often can be simplified by manipulating the model equations. Algebraic manipulations including nonlinear transformations of model parameters, do not change the numerical result of the adjustment and can be a powerful method to improve the performance of solution algorithms. Nonlinear transformations of the observations, on the other hand, do change the numerical results unless the normal equations are transformed accordingly. The latter transformation has been neglected by previous authors and this article provides a complete set of formulas that are needed to implement transformations of observations. The transformations are in general less useful than parameter transformations for the improvement of algorithms but may have other applications in particular situations.     

Reverse Foldovers for Blocked 2 m−k Fractional Factorial Designs

Two-level regular fractional factorial designs are often used in industry as screening designs to help identify early on in an experimental process those experimental or system variables which have significant effects on the process being studied. When the experimental material to be used in the experiment is heterogenous or the experiment must be performed over several well-defined time periods, blocking is often used as a means to improve experimental efficiency by removing the possible effects of heterogenous experimental material or possible time period effects. In a recent article, Li and Jacroux (2007 Li , F. , Jacroux , M. (2007). Optimal foldover plans for blocked 2 ^m?k fractional factorial designs. J. Statsist. Plann. Infer 137:2434–2452. [Google Scholar]) suggested a strategy for constructing optimal follow-up designs for blocked fractional factorial designs using the well-known foldover technique in conjunction with several optimality criteria. In this article, we consider the reverse foldover problem for blocked fractional factorial designs. In particular, given a 2^(m+p)?(p+k) blocked fractional factorial design D, we derive simple sufficient conditions which can be used to determine if there exists a 2^{(m+p?1)?(p?1+k+1)} initial fractional factorial design d which yields D as a foldover combined design as well how to generate all such d. Such information is useful in developing an overall experimental strategy in situations where an experimenter wants an overall blocked fractional factorial design with “desirable” properties but also wants the option of analyzing the observed data at the halfway mark to determine if the significant experimental variables are obvious (and the experiment can be terminated) or if a different path of experimentation should be taken from that initially planned.     

Orthogonal [k − 1, k + 1]-factorizations in graphs

Let G be a graph. Let F={F₁,F₂,...F_d} be a factorization of G and H be a subgraph of G. If H has exactly one edge in common with F_i for all i = 1,2,…,d, then we say that F is orthogonal to H. In this paper it is proved that for any d-matching M of a [kd − 1, kd + 1]-graphG, there is a [k − 1, k + 1]-factorization of G orthogonal to M where k ⩾ 2 is an integer.     

Estimation of p{y p> max(y1, y2, …, yp-1)}in theexponential case

This paper deals with the derivation of (i) the MLE (ii) the MVUE (iii) a Bayes estimator of the probability in the title, for the case p = 2. Simulation studies are carried out to compare these estimators. The results suggest that the MLE and the Bayes estimator are biased and the Bayes estimator have the smallest MSE. In the general case, explicit expression for the probability in the title is derived and the MLE and Bayes estimator are obtained. A general method of deriving the MVUE is pointed out. Because of the simulation studies for p = 2 it is recommended that the Bayes or predictive estimator should be used.     

Conditional logistic regression in cluster-specific 1: m matched treatment–control designs

Conditional logistic regression is a popular method for estimating a treatment effect while eliminating cluster-specific nuisance parameters when they are not of interest. Under a cluster-specific 1: m matched treatment–control study design, we present a new closed-form relationship between the conditional logistic regression estimator and the ordinary logistic regression estimator. In addition, we prove an equivalence between the ordinary logistic regression and the conditional logistic regression estimators, when the clusters are replicated infinitely often, which indicates that potential bias concerns when applying conditional logistic regression to complex survey samples.