Lower bounds on expectations of positive L-statistics from without-replacement models

We consider samples drawn without replacement from finite populations. We establish optimal lower non-negative and upper non-positive bounds on the expectations of linear combinations of order statistics centered about the population mean in units generated by the population central absolute moments of various orders. We also specify the general results for important examples of sample extremes, Gini mean differences and sample range. The paper completes the results of Papadatos and Rychlik [2004. Bounds on expectations of L-statistics from without replacement samples. J. Statist. Plann. Inference 124, 317–336], where sharp negative lower and positive upper bounds on the expectations of the combinations were presented for the without-replacement samples.     

Two-stage Huber estimation

In this paper we propose a new robust estimator in the context of two-stage estimation methods directed towards the correction of endogeneity problems in linear models. Our estimator is a combination of Huber estimators for each of the two stages, with scale corrections implemented using preliminary median absolute deviation estimators. In this way we obtain a two-stage estimation procedure that is an interesting compromise between concerns of simplicity of calculation, robustness and efficiency. This method compares well with other possible estimators such as two-stage least-squares (2SLS) and two-stage least-absolute-deviations (2SLAD), asymptotically and in finite samples. It is notably interesting to deal with contamination affecting more heavily the distribution tails than a few outliers and not losing as much efficiency as other popular estimators in that case, e.g. under normality. An additional originality resides in the fact that we deal with random regressors and asymmetric errors, which is not often the case in the literature on robust estimators.     

Generalized Laplacian approximations in Bayesian inference

This paper presents a new Laplacian approximation to the posterior density of η = g(θ). It has a simpler analytical form than that described by Leonard et al. (1989). The approximation derived by Leonard et al. requires a conditional information matrix R_η to be positive definite for every fixed η. However, in many cases, not all R_η are positive definite. In such cases, the computations of their approximations fail, since the approximation cannot be normalized. However, the new approximation may be modified so that the corresponding conditional information matrix can be made positive definite for every fixed η. In addition, a Bayesian procedure for contingency-table model checking is provided. An example of cross-classification between the educational level of a wife and fertility-planning status of couples is used for explanation. Various Laplacian approximations are computed and compared in this example and in an example of public school expenditures in the context of Bayesian analysis of the multiparameter Fisher-Behrens problem.     

Test for homogeneity in Hardy–Weinberg normal mixture model

The phenotype of a quantitative trait locus (QTL) is often modeled by a finite mixture of normal distributions. If the QTL effect depends on the number of copies of a specific allele one carries, then the mixture model has three components. In this case, the mixing proportions have a binomial structure according to the Hardy–Weinberg equilibrium. In the search for QTL, a significance test of homogeneity against the Hardy–Weinberg normal mixture model alternative is an important first step. The LOD score method, a likelihood ratio test used in genetics, is a favored choice. However, there is not yet a general theory for the limiting distribution of the likelihood ratio statistic in the presence of unknown variance. This paper derives the limiting distribution of the likelihood ratio statistic, which can be described by the supremum of a quadratic form of a Gaussian process. Further, the result implies that the distribution of the modified likelihood ratio statistic is well approximated by a chi-squared distribution. Simulation results show that the approximation has satisfactory precision for the cases considered. We also give a real-data example.     

RuCl2[P(C6H5)3]2(NH2CH2CH2NH2)催化苯乙酮加氢反应的研究

优化了以RuCl2[P(C6H5)3]2(NH2CH2CH2NH2)作催化剂催化苯乙酮加氢制备α-苯乙醇的反应条件,考察了反应温度、反应压力、碱的用量及不同的碱对反应的影响,得出了一个较好的反应条件.     

同工异曲的悲歌--《菊花的幽香》与《薄奠》之比较

英国小说大师劳伦斯创作的<菊花的幽香>和中国著名小说家郁达夫创作的<薄奠>具有异曲同工之处,他们分别以象征和写实的笔法描写了一个以男主人公的死亡为结局的家庭悲剧,并对各自社会的罪恶进行了揭露,因而具有进步意义,成为中英文学史上不可多得的佳作.     

对张学良联共抗日思想形成的几点思考

指出中华民族的千古功臣张学良将军,是中国共产党人的一位真正朋友。论述了张学良联共抗日的思想基础、形成及其实现联共抗日的途径。同时,对张学良联共抗日思想与行动进行了评析,从而为学术界进一步研究和评价张学良将军与中国共产党人的关系提供了借鉴。     

新硼试剂3—甲氧基—甲亚胺H与硼显色反应的研究

对新硼试剂3-甲氧基-甲亚胺H与硼显色反应体系研究结果表明,在pH=5的醋酸-醋酸铵缓冲体系中,硼与3-甲氧基-甲亚胺H在常温下形成2:3的黄绿色配合物,配合物稳定24h以上,λmax=410nm,ε550=6.82×104cm·mol-1·L-1,硼含量在0～2.5μg/25mL范围符合比耳定律.     

On the asymptotic normality of the L1- and L2-errors in histogram density estimation

The L₁ and L₂-errors of the histogram estimate of a density f from a sample X₁,X₂,…,Xn using a cubic partition are shown to be asymptotically normal without any unnecessary conditions imposed on the density f. The asymptotic variances are shown to depend on f only through the corresponding norm of f. From this follows the asymptotic null distribution of a goodness-of-fit test based on the total variation distance, introduced by Györfi and van der Meulen (1991). This note uses the idea of partial inversion for obtaining characteristic functions of conditional distributions, which goes back at least to Bartlett (1938).     

Generalized partially linear varying-coefficient models

Generalized varying-coefficient models are useful extensions of generalized linear models. They arise naturally when investigating how regression coefficients change over different groups characterized by certain covariates such as age. In this paper, we extend these models to generalized partially linear varying-coefficient models, in which some coefficients are constants and the others are functions of certain covariates. Procedures for estimating the linear and non-parametric parts are developed and their associated statistical properties are studied. The methods proposed are illustrated using some simulations and real data analysis.