The analysis of dependence for three ways contingency tables with ordinal variables: A case study of patient satisfaction data

For many questionnaires and surveys in the marketing, business, and health disciplines, items often involve ordinal scales (such as the Likert scale and rating scale) that are associated in sometimes complex ways. Techniques such as classical correspondence analysis provide a simple graphical means of describing the nature of the association. However, the procedure does not allow the researcher to specify how one item may be associated with another, nor does the analysis allow for the ordinal structure of the scales to be reflected. This article presents a graphical approach that can help the researcher to study in depth the complex association of the items and reflect the structure of the items. We will demonstrate the applicability of this approach using data collected from a study that involves identifying major factors that influence the level of patient satisfaction in a Neapolitan hospital.     

利用"取点法"测量绘图软件中非标准几何体尺寸

研究了测量计算机绘图软件中非标准几何体尺寸的问题.首先阐述了利用绘图软件对非标准几何体的预处理方法,然后根据各种几何体的特性及插值理论,推导出了测取绘图软件中非标准几何体尺寸的"取点法",并以计算机绘图软件中的三个几何体为例,对该方法进行了验证,其结果表明了此种方法的可靠性.     

美洛昔康滴丸成型工艺研究

目的优选美洛昔康滴丸最佳成型工艺。方法对基质、冷凝液的选择采用单因素试验法进行研究;对滴制工艺的选择采用正交试验法,以丸重RSD和圆整度为考察指标,对滴制温度、滴制距离、冷凝剂温度和冷凝剂高度等因素进行研究。结果以PEG6000为基质,以液体石蜡为冷凝剂,美洛昔康与PEG6000以1∶7的比例混合,80 ℃保温滴于高度60 cm以上、温度5 ℃的冷凝剂中,滴距8 cm。结论以该工艺制备的美洛昔康滴丸成型性与质量均较好。     

违犯Bell不等式的正交态及非正交态的量子缠绕

本文给出正交态及非正交态的量子缠绕，通过分析两个实例，发现能够产生不遵守Bell不等式最大限度的缠绕态。     

A counterexample to a conjecture on random shadows

We construct a counterexample to a conjecture in stereology. It is well known that two convex solid bodies which cast congruent orthographic shadows on any common plane must necessarily be congruent to each other. This characterization fails if the orientations of the shadows are allowed to differ. Such counterexamples as have been constructed for the latter case fail to have the same distribution of random shadows projected onto planes with random orientation. Therefore P. McCullagh has conjectured that two bodies whose random shadows have the same distribution are necessarily congruent. We construct a counterexample to this conjecture. Some implications are drawn for the development of a general theory of stereological reconstruction based upon random projected shadows or images.     

关于欧氏空间中的线性变换

本文给出了欧氏空间的变换是线性变换的几个充分条件,进而导出了欧氏空间的变换是正交变换的四个充要条件。     

Data depths satisfying the projection property

Summary: Data depth is a concept that measures the centrality of a point in a given data cloud x ₁, x ₂,...,x _n or in a multivariate distribution P ^X on ^{d d} . Every depth defines a family of so–called trimmed regions. The –trimmed region is given by the set of points that have a depth of at least . Data depth has been used to define multivariate measures of location and dispersion as well as multivariate dispersion orders.If the depth of a point can be represented as the minimum of the depths with respect to all unidimensional projections, we say that the depth satisfies the (weak) projection property. Many depths which have been proposed in the literature can be shown to satisfy the weak projection property. A depth is said to satisfy the strong projection property if for every the unidimensional projection of the –trimmed region equals the –trimmed region of the projected distribution.After a short introduction into the general concept of data depth we formally define the weak and the strong projection property and give necessary and sufficient criteria for the projection property to hold. We further show that the projection property facilitates the construction of depths from univariate trimmed regions. We discuss some of the depths proposed in the literature which possess the projection property and define a general class of projection depths, which are constructed from univariate trimmed regions by using the above method.Finally, algorithmic aspects of projection depths are discussed. We describe an algorithm which enables the approximate computation of depths that satisfy the projection property.     

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.