Optimal designs for covariates’ models

A linear model with one treatment at V levels and first order regression on K continuous covariates with values on a K-cube is considered. The D-criterion is used to judge the ‘goodness’ of any design for estimating the parameters of this model. Since this criterion is based on the determinant of the information matrix M(d) of a design d, upper bounds for |M(d)| yield lower bounds for the D-efficiency of any design d in estimating the vector of parameters in the model. We consider here only classes of designs d for which the number N of observations to be taken is a multiple of V, that is, there exists R≥2 such that N=V×R.Under these conditions, we determine the maximum of |M(d)|, and conditions under which the maximum is attained. These conditions include R being even, each treatment level being observed the same number of times, that is, R times, and N being a multiple of four. For the other cases of congruence of N (modulo 4) we further determine upper bounds on |M (d)| for equireplicated designs, i.e. for designs with equal number of observations per treatment level. These upper bounds are shown to depend also on the congruence of V (modulo 4). For some triples (N,V,K), the upper bounds determined are shown to be attained.Construction methods yielding families of designs which attain the upper bounds of |M(d)| are presented, for each of the sixteen cases of congruence of N and V.We also determine the upper bound for D-optimal designs for estimating only the treatment parameters, when first order regression on one continuous covariate is present.     

Construction of (M,S)-optimal design for block size 3

(M,S)-optimal designs are constructed for block size three when the number of treatments is of the form 6t + 3.     

A construction for generalized hadamard matrices

We prove that if p^r and p^r ? 1 are both prime powers then there is a generalized Hadamard matrix of order p^r(p^r ? 1) with elements from the elementary abelian group Z_p x?x Z_p. This result was motivated by results of Rajkundia on BIBD's. This result is then used to produce p^r ? 1 mutually orthogonal F-squares F(p^r(p^r ? 1); p^r ? 1).     

The family of t-designs - part II

This is a continuation of Part I of our previous paper (1980) on conbinatorial aspects of t-designs with t ≥ 2. Along the same developments as in Part I, this paper provides tables, assorted examples of t-designs, and interesting unsolved problems. A brief background and a short review of the literature related to each unsolved problem is also provided. Some tables list parameters of designs whose existence or nonexistence is not established in literature. Notation and numbering of Part I are still used here.     

Large sample theory of the Langevin distribution

The Langevin (or von Mises-Fisher) distribution of random vector x on the unit sphere ω_q in $\text{R}$^q has a density proportional to exp κμ'x where μ'x is the scalar product of x with the unit modal vector μ and κ?0 is a concentration parameter. This paper studies estimation and tests for a wide variety of situations when the sample sizes are large. Geometrically simple test statistics are given for many sample problems even when the populations may have unequal concentration parameters.     

Antipodally symmetric distributions for orientation statistics

The conventional antipodally symmetric Bingham matrix distribution on the Stiefel manifold is generalized. Large sample maximum likelihood estimation and uniformity tests are discussed, and a parametric model for axial orientations (X-shapes) is suggested. A generalization of the Khatri-Mardia matrix distribution is developed to provide a model suitable for hybrids (T-shapes).     

我国农民工城市化问题阐析

随着中央政府对农民工城市化在整体上由限制转入鼓励以来,各地方政府竞相推出了促进农民工城市化的个性方案。通过对农民工城市化宏观层面上整体判断,中观层面上体制制约因素,微观层面上农民工成本支付能力,以及地方政府激励相容性的阐析得出:成本支付是农民工城市化问题的核心,而在城乡统筹前提下的农民工自由选择权是关键。在农民工城市化的过程中,政府既不能缺位,也不能越位,不应该制定功利性的目标和政策。     

中职语文教学中激发学生兴趣的策略与方法探究

学习兴趣是保证学生有效学习发生的重要因素,培养学生的学习兴趣是提高教学质量的重要方面。通过对中职学生能力素质实际、专业发展需要方面的讨论,就在教学过程中激发学生兴趣的教学策略与教学方法展开探究,并结合实际提出此过程中应注意的问题。     

浅谈本部中等职业学校教师现代教育技术态度的形成

本文分析了中等职业学校教师现代教育技术的态度和形成过程,提出了中等职业学校教师要加强现代教育思想观念,加强对现代教育技术的宣传和培训,从现代教育技术的使用等方面来培养教师现代教育技术的积极态度。     

A Remedy for Kernel Estimation Under Random Design

Two common kernel-based methods for non-parametric regression estimation suffer from well-known drawbacks when the design is random. The Gasser-Müller estimator is inadmissible due to its high variance while the Nadaraya-Watson estimator has zero asymptotic efficiency because of poor bias behavior. Under asymptotic consideration, the local linear estimator avoids these two drawbacks of kernel estimators and achieves minimax optimality. However, when based on compact support kernels its finite sample behavior is disappointing because sudden kinks may show up in the estimate.

This paper proposes a modification of the kernel estimator, called the binned convolution estimator leading to a fast O(n) method. Provided the design density is continously differentiable and the conditional fourth moments exist the binned convolution estimator has asymptotic properties identical with those of the local linear estimator.