Parameter estimation of state space models for univariate observations

This paper contributes to the problem of estimation of state space model parameters by proposing estimators for the mean, the autoregressive parameters and the noise variances which, contrarily to maximum likelihood, may be calculated without assuming any specific distribution for the errors. The estimators suggested widen the scope of the application of the generalized method of moments to some heteroscedastic models, as in the case of state-space models with varying coefficients, and give sufficient conditions for their consistency. The paper includes a simulation study comparing the proposed estimators with maximum likelihood estimators. Finally, these methods are applied to the calibration of the meteorological radar and estimation of area rainfall.     

Lattice path combinatorics for multiple product identities

Lattice paths are enumerated as walks on a lattice under the Delannoy criterion of vertical, horizontal and upward diagonal steps. Delannoy recursions are generalized for arbitrary weights in each of these directions, where the row elements of the Delannoy triangles correspond to lattice paths for all walks at a given length.     

Generalized Linear Models

The importance of random number generators has increased over the years. This follows from the fact that contemporary research methods rely more and more on simulation and the increased importance of encryption technology. The output of a random number generator is created by either an algorithm or a physical device. The most popular method for random number generation is through the use of an algorithm. This article presents a new category of physical random bit generator that is packaged by several manufacturers. A statistical analysis of the output from the generators is given.     

Nonparametric regression with cross‐classified responses

In this article, we develop regression models with cross‐classified responses. Conditional independence structures can be explored/exploited through the selective inclusion/exclusion of terms in a certain functional ANOVA decomposition, and the estimation is done nonparametrically via the penalized likelihood method. A cohort of computational and data analytical tools are presented, which include cross‐validation for smoothing parameter selection, Kullback–Leibler projection for model selection, and Bayesian confidence intervals for odds ratios. Random effects are introduced to model possible correlations such as those found in longitudinal and clustered data. Empirical performances of the methods are explored in simulation studies of limited scales, and a real data example is presented using some eyetracking data from linguistic studies. The techniques are implemented in a suite of R functions, whose usage is briefly described in the appendix. The Canadian Journal of Statistics 39: 591–609; 2011. © 2011 Statistical Society of Canada     

基于区间数大小不能直接判定的灰矩阵博弈的策略优超及其最优解研究

对于区间灰数大小不能直接判定的灰矩阵博弈G(⊗)={S₁,S₂,A(⊗)}问题,其策略优超和纯策略求解问题的关键在于A(⊗)中区间灰数大小判定准则的设定与判定方法的设计。本文运用灰色系统思想和系统工程的理论,揭示了人们在灰信息条件下的博弈心理与博弈决策规则,根据区间灰数势关系的判定规则,提出了灰数势意义下的策略优超法则,定义了纯策略解。最后,以商业银行贷款动态损失准备金计提为案例,对其灰势意义下的策略优超和纯策略解问题进行了研究。     

理想气体微观状态数的计算及其统计性质的研究

本文借助自由粒子的量子能态分布理论,利用3n维空间球体模型,实现了对理想气体（N,V,E）系统微态数的计算,在此基础上,给出了理想气体热力学量的统计结果。     

Optimal estimation of a finite population mean under generalized random permutation models

Employing certain generalized random permutation models and a general class of linear estimators of a finite population mean, it is shown that many of the conventional estimators are “optimal” in the sense of minimum average mean square error. Simple proofs are provided by using a well-known theorem on UMV estimation. The results also cover certain simple response error situations.     

The Independence Number of Graphs with a Forbidden Cycle and Ramsey Numbers

Let k 5 be a fixed integer and let m = (k – 1)/2. It is shown that the independence number of a C _k-free graph is at least c ₁[ d(v)^{1/(m – 1)}]^{(m – 1)/m} and that, for odd k, the Ramsey number r(C _k, K _n) is at most c ₂(n ^{m + 1}/log n)^1/m , where c ₁ = c ₁(m) > 0 and c ₂ = c ₂(m) > 0.     

神秘数字“七”再发微

本文以数字"七"在中国民俗中的广泛应用为表象,依据我国古代先哲对宇宙天体运动节律(即"天道唯七")和人体生命节律(7—8年)的认识,以及现代医学对人的生物节律的进一步确认,指出数字"七"之所以具有宇宙数字的性质及巫术的、神话的意义,"获得模式数字的资格",根本原因在于它体现了以上两个节律。