A Note on the Predictors of Differenced Sequences

In this note we consider the problems of optimal linear prediction (o.l.p.) and the minimum mean squared error prediction (m.m.s.e.p.) of a sequence X_t, which fits to a stationary and invertible ARMA model through the filter (1 - B^s)^d X_t= Y_t. It is shown that these two predictors are not identical in general from the theoretical point of view. Permitting the degree of differencing d to take any real value, a set of conditions for these commonly applied prediction formulas to be identical is given.     

关于一个Brauer定理的注记

研究一个被广泛引用的Ｂｒａｕｅｒ定理，指出该定理是错误的；讨论了特征值估计理论中常涉及的卵形Ｄｉ，ｊ＝｛ｚ∈Ｃ∶｜ｚ－ａｉ‖ｚ－ａｊ｜≤ＲｉＲｊ，ｉ≠ｊ｝，其中Ａ＝（ａｉｊ）∈Ｃｎ，ｎ，得到了关于Ｄｉｊ和矩阵特征值的有关结论，从理论上说明了Ｂｒａｕｅｒ定理错误的原因。     

Partitioned algorithms for maximum likelihood and other non-linear estimation

There are a variety of methods in the literature which seek to make iterative estimation algorithms more manageable by breaking the iterations into a greater number of simpler or faster steps. Those algorithms which deal at each step with a proper subset of the parameters are called in this paper partitioned algorithms. Partitioned algorithms in effect replace the original estimation problem with a series of problems of lower dimension. The purpose of the paper is to characterize some of the circumstances under which this process of dimension reduction leads to significant benefits.Four types of partitioned algorithms are distinguished: reduced objective function methods, nested (partial Gauss-Seidel) iterations, zigzag (full Gauss-Seidel) iterations, and leapfrog (non-simultaneous) iterations. Emphasis is given to Newton-type methods using analytic derivatives, but a nested EM algorithm is also given. Nested Newton methods are shown to be equivalent to applying to same Newton method to the reduced objective function, and are applied to separable regression and generalized linear models. Nesting is shown generally to improve the convergence of Newton-type methods, both by improving the quadratic approximation to the log-likelihood and by improving the accuracy with which the observed information matrix can be approximated. Nesting is recommended whenever a subset of parameters is relatively easily estimated. The zigzag method is shown to produce a stable but generally slow iteration; it is fast and recommended when the parameter subsets have approximately uncorrelated estimates. The leapfrog iteration has less guaranteed properties in general, but is similar to nesting and zigzagging when the parameter subsets are orthogonal.     

Measuring multimodality

Existing sample statistics do little to address the question of multimodality, a question which is interesting in itself and which also arises in exploratory multivariate data analysis using projection pursuit. We propose a new index more strongly geared to the specific task of measuring multimodality than other sample statistics known to us, we show how to compute it, explore its properties, and consider its generalisation to the multivariate case. The behaviour of the index is illustrated by some simple numerical examples.     

指示语的自我中心性和指示映射现象

指示语是语言和语境的关系在语言结构中的反映,对指示语的理解关系到交际双方能否进行有效的自我表达和相互沟通。自我中心性是指示语最基本的特性,但在实际使用过程中也存在指示映射现象,后者可利用心理空间理论对其从认知角度进行解释。     

The automatic percentile method: Accurate confidence limits in parametric models

The problem of constructing confidence limits for a scalar parameter is considered. Under weak conditions, Efron's accelerated bias-corrected bootstrap confidence limits are correct to second order in parametric familles. In this article, a new method, called the automatic percentile method, for setting approximate confidence limits is proposed as an attempt to alleviate two problems inherent in Efron's method. The accelerated bias-corrected method is not fully automatic, since it requires the calculation of an analytical adjustment; furthermore, it is typically not exact, though for many situations, particularly scalar-parameter familles, exact answers are available. In broader generality, the proposed method is exact when exact answers exist, and it is second-order accurate otherwise. The automatic percentile method is automatic, and for scalar parameter models it can be iterated to achieve higher accuracy, with the number of computations being linear in the number of iterations. However, when nuisance parameters are present, only second-order accuracy seems obtainable.     

应用正交试验法优选电火花成型加工电参数的研究

用正交试验法研究了电火花成型加工中电参数与工件加工速度、表面粗糙度和工具电极损耗比等工艺指标的关系，提出了优选的电参数方案．     

The crystallization of a paranoid symptom: Three theories

The dynamics of paranoia are complex. The cognitive and behavioral patterns of paranoia are well documented in the clinical literature. However, writings on the etiology of paranoia are sparse. Sigmund Freud, Melanie Klein, and William W. Meissner are the three most comprehensive and recognized theorists on the etiology and psychodynamic functions of paranoia. Their theories are delineated and applied to a clinical vignette of a woman with a recently developed paranoid symptom.     

催化剂粒内组份浓度分布的正交配点计算法

本文采用正交配点法计算了在固体催化剂上进行n级不可逆反应及n级可逆反应时,催化剂颗粒内组份的浓度分布,并与解析法进行了比较。当配置点数N=3,且满足取权函数W(R′~2)=1-R′~2时的近似解较接近解析解。