Partitions of point processes: Multivariate poisson approximations

This study shows that when a point process is partitioned into certain uniformly sparse subprocesses, then the subprocesses are asymptotically multivariate Poisson or compound Poisson. Bounds are given for the total-variation distance between the subprocesses and their limits. Several partitioning rules are considered including independent, Markovian, and batch assignments of points.     

Invariant tests for symmetry about an unspecified point based on the empirical characteristic function

This paper considers a flexible class of omnibus affine invariant tests for the hypothesis that a multivariate distribution is symmetric about an unspecified point. The test statistics are weighted integrals involving the imaginary part of the empirical characteristic function of suitably standardized given data, and they have an alternative representation in terms of an L²-distance of nonparametric kernel density estimators. Moreover, there is a connection with two measures of multivariate skewness. The tests are performed via a permutational procedure that conditions on the data.     

Asymptotic optimality of nonparametric tests for restricted alternatives in some multivariate mixed models

For some mixed models (involving both stochastic and nonstochastic predictors), a general class of permutationally distribution-free rank tests for some restricted alternative problems is considered. The proposed tests are asymptotically optimal in the light of the restricted likelihood ratio tests. For an ordered alternative problem in a two-way analysis of covariance model, the proposed tests are asymptotically optimal.     

Multiparameter estimation for some multivariate discrete distributions with possibly dependent components

Summary In multiparameter estimation for multivariate discrete distributions with infinite support, inadmissibility problems in situations where the multivariate probability distribution function isnot a product of the one-dimensional marginal probability distribution functions have previously been unexplored. This paper examines the inadmissibility problem in some of these situations. Special attention is given to estimating the mean of a negative multinomial distribution. In estimating the mean vector, certain Clevenson-Zidek type estimators are shown to be uniformly better than the usual estimator under a large class of generally scaled squared loss functions. Some of the results are generalized to other multivariate discrete distributions and to situations where several independent negative multinomial distributions are considered.     

Linear Discrimination with Adaptive Ridge Classification Rules

This article considers the use of adaptive ridge classification rules for classifying an observation as coming from one of two multivariate normal distributionsN(μ⁽¹⁾, Σ) andN(μ⁽²⁾, Σ). In particular, the asymptotic expected error rates for a general class of these rules are obtained and are compared with that of the usual linear discriminant rule.     

多项式空间的对偶及其在多元插值中的应用

本文通过把域Ｋ上ｎ元多项式环看成域Ｋ上的无限维向量空间Ａ，把ｎ维仿射空间Ｋ＾ｎ中的每一点看成Ａ上的线性泛函，从而Ｋ＾ｎ为对偶空间Ａ＾＊的子集，利用对偶空间的理论得到了一些有趣的理论结果，弄清了Ｋ＾ｎ上点有限拓扑的结构，给出了判定给定结点组是否是给定多项式空间的适定结点组的判定准则，最后还给出了构造理想对偶基的一种算法。     

Good Lattice Rules in Weighted Korobov Spaces with General Weights

We study the problem of multivariate integration and the construction of good lattice rules in weighted Korobov spaces with general weights. These spaces are not necessarily tensor products of spaces of univariate functions. Sufficient conditions for tractability and strong tractability of multivariate integration in such weighted function spaces are found. These conditions are also necessary if the weights are such that the reproducing kernel of the weighted Korobov space is pointwise non-negative. The existence of a lattice rule which achieves the nearly optimal convergence order is proven. A component-by-component (CBC) algorithm that constructs good lattice rules is presented. The resulting lattice rules achieve tractability or strong tractability error bounds and achieve nearly optimal convergence order for suitably decaying weights. We also study special weights such as finite-order and order-dependent weights. For these special weights, the cost of the CBC algorithm is polynomial. Numerical computations show that the lattice rules constructed by the CBC algorithm give much smaller worst-case errors than the mean worst-case errors over all quasi-Monte Carlo rules or over all lattice rules, and generally smaller worst-case errors than the best Korobov lattice rules in dimensions up to hundreds. Numerical results are provided to illustrate the efficiency of CBC lattice rules and Korobov lattice rules (with suitably chosen weights), in particular for high-dimensional finance problems.     

SOME MULTIVARIATE DMRL AND NBUE DEFINITIONS BASED ON CONDITIONAL STOCHASTIC ORDER

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Syringe-to-syringe-dispersive liquid–phase microextraction combined with flame atomic absorption spectrometry for pre-concentration and determination of cobalt with the aid of experimental design

A rapid and selective technique has been proposed for the extraction, pre-concentration and determination of trace amounts of cobalt in water and pharmaceutical samples by syringe-to-syringe-dispersive liquid–phase microextraction (SS-DLPME) combined with flame atomic absorption spectrometry (FAAS). In the developed method, 1-nitroso-2-naphthol was used as a selective complexing agent and 1-octanol was selected as the extraction solvent. Factors such as pH of the sample solution, concentration of the complexing agent, volume of the extraction solvent, number of injections and centrifugation time affecting the extraction efficiency were screened using a Plackett–Burman design (PBD) and optimised using a Box–Behnken design (BBD). Under optimum conditions, a dynamic linear range of 2.5–650 μg L^?1 with the coefficient of determination r² = 0.997 was obtained. The resultant limit of detection (LOD) was 0.68 μg L^?1, whereas the enrichment factor (EF), intraday precision and inter-day precision were 281, 1.43% and 1.93%, respectively. This method was used successfully for pre-concentration and determination of the analyte in environmental water and drug samples.