OnL p -convergence rates for statistical functions with application toL-estimates

Summary A parameter which may be represented as a functionalT(F) of a distribution functionF may be estimated by the “statistical function”T(F _n ), whereF _n is the empirical distribution function. Recently, Boos and Serfling (1979, Florida State University Statistics Report No. M 499) obtained sufficient conditions for the Berry-Esseen theorem to hold forT(F _n )-T(F) and applied the results to derive rates of convergence inL _∞ forL-estimates. The present note complements their work by obtaining theL _p -rates of convergence, 1≦p<∞ forT(F _n )-T(F) and its application toL-estimates.     

A disjoint disks property for 3-manifolds

We show that the map separation property (MSP), a concept due to H.W. Lambert and R.B. Sher, is an appropriate analogue of J.W. Cannon’s disjoint disks property (DDP) for the class $\text{C}$ of compact generalized 3-manifolds with zero-dimensional singular set, modulo the Poincaré conjecture. Our main result is that the Poincaré conjecture (in dimension three) is equivalent to the conjecture that every X?$\text{C}$ with the MSP is a topological 3-manifold.     

Factorizing multivariate time series operators

Motivated by problems occurring in the empirical identification and modelling of a n-dimensional ARMA time series X(t) we study the possibility of obtaining a factorization (I + a₁B + … + a_pB^p) X(t) = [Π_i=1^p (I ? α_iB)] X(t), where B is the backward shift operator. Using a result in [3] we conclude that as in the univariate case such a factorization always exists, but unlike the univariate case in general the factorization is not unique for given a₁, a₂,…, a_p. In fact the number of possibilities is limited upwards by $\text{(np)!}\text{(n!)}{}^{\mathrm{p}}$, there being cases, however, where this maximum is not reached. Implications for the existence and possible use of transformations which removes nonstationarity (or almost nonstationarity) of X(t) are mentioned.     

The category of Urysohn spaces is not cowellpowered

It is shown that the category of Urysohn spaces and continuous maps is not cowellpowered. To this end we will construct for each ordinal number β a Urysohn space Y_β with card $\text{(Y}{}_{\mathrm{\beta }}\text{= ?}{}_0\text{?}\text{card}\text{(β)}$ and a continuous map $\text{e}{}_{\mathrm{\beta }}\text{:}\text{Q}\text{→ Y}{}_{\mathrm{\beta }}$ from the rationals into Y_β. It turns out that $\text{e}{}_{\mathrm{\beta }}$ is an external monomorphism in the category of Hausdorff spaces and an epimorphism in the category of Urysohn spaces.     

一类非平稳m相依序列收敛于正态的非一致速率

本文在随机变量的矩母函数存在或者矩母函数不存在但各阶矩有限的条件下，讨论了一类非平稳ｍ相依的随机变量序列的标准化和分布收敛于正态分布的非一致速率。     

Salze von Halogenophosphorsäuren XIX [1] Über die Bildung und den Nachweis stabiler Intermediate bei der Reaktion von Fluorid mit Phosphoroxidchlorid

Salts of Halogenophosphoric Acids. XIX Formation and Identification of Stable Intermediates on the Reaction of Fluoride with Phosphorus Oxychloride By reaction of POCl₃ with fluorides of tertiary amines in the presence of the free amines the oxo-fluorophosphates [F₂P(O? O? PF₅)]^?, [OPF₅]^2?, and [OPF₄]^? are formed as intermediates on the way to [PF₆]^?. The compounds were characterized by NMR spectroscopy.