修正Weyl型算子的L~2连续性的证明方法

对文献[1]中Wcyl型拟微分算子的L~2连续性的证明方法中的一个错误进行了修正。利用在象征中加入衰减因子的方法,得到了正确的证明。     

Projector operators in the multivariate Zyskind-Martin model

Summary Two quadratic formsS _H andS _E for a testable hypothesis and for an error in the multivariate Zyskind-Martin model with singular covariance matrix are expressed by means of projector operators. Thus the results for the multivariate standard model with identity covariance matrix given by Humak (1977) and Christensen (1987, 1991) are generalized for the case of Zyskind-Martin model. Special cases of our results are formulae forS _H andS _E in Aitken's (1935) model. In the case of general Gauss-Markoff modelS _H andS _E can also be expressed by means of projector operators for some subclasses of testable hypotheses. For these hypotheses, testing in Gauss-Markoff model is equivalent to testing in a Zyskind-Martin model.     

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.     

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。     

国有企业经营者选择中的识别风险及其规避

当前,我们对国有企业经营者的选拔存在极大的风险,这种风险主要表现在对经营者能力及素质的识别上.可通过"专业对口"、动态考察、实际检验、公开招聘等途径去规避识别风险,选择到最合格的经营者.当发现对经营者的选择出现失误时,"双重竞争机制"、竞争性经理市场和"进入-退出"机制的建立,可起到"亡羊补牢"的作用.     

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。     

Vec and vech operators for matrices,with some uses in jacobians and multivariate statistics

The vec of a matrix X stacks columns of X one under another in a single column; the vech of a square matrix X does the same thing but starting each column at its diagonal element. The Jacobian of a one-to-one transformation X → Y is then ∣∣?(vecX)/?(vecY) ∣∣ when X and Y each have functionally independent elements; it is ∣∣ ?(vechX)/?(vechY) ∣∣ when X and Y are symmetric; and there is a general form for when X and Y are other patterned matrices. Kronecker product properties of vec(ABC) permit easy evaluation of this determinant in many cases. The vec and vech operators are also very convenient in developing results in multivariate statistics.