Jacob Wolfowitz (1910–1981)

The dependence of inferences about the difference of means on assumptions about the variance ratio p ² is considered, with special reference to the assumption that p = 1.     

L氏(P氏)动态物价指数模型探析

Ｌ氏（Ｐ氏）动态物价指数模型探析□文／赵培标一问题的提出Ｌ氏（Ｐ氏）指数系指意大利统计学家拉斯贝尔（Ｌａｓｐｅｙｒｅｓ）提出的以基期消费品的数量为权数的拉氏物价指数（Ｐ氏指数，系指法国统计学家派煦（Ｐａｓｃｈｅ）提出的以报告期消费品的数量为权数的派...     

中华人民共和国国家统计局关于发展国民经济的第一个五年(1953年到1957年)计划执行结果的公报(1959年4月13日)

我国从1953年开始执行的发展国民经济的第一个五年计划,在中共中央和毛主席的领导下,经过全国各族人民的辛勤努力,并且得到了苏联和其他兄弟国家的援助,到1957年底已经胜利地超额完成了.第一个五年计划的胜利完成,使我国在社会主义改造和社会主义建设两个方面都取得了巨大的成就.我国社会经济结构和国民经济面貌已经发生了重大的变化.在党的从资本主义到社会主义过渡时期总路线     

Information Properties for Concomitants of Order Statistics in Farlie–Gumbel–Morgenstern (FGM) Family

Let (X _i , Y _i ), i = 1, 2,…, n be independent and identically distributed random variables from some continuous bivariate distribution. If X _(r) denotes the rth-order statistic, then the Y's associated with X _(r) denoted by Y _[r] is called the concomitant of the rth-order statistic. In this article, we derive an analytical expression of Shannon entropy for concomitants of order statistics in FGM family. Applying this expression for some well-known distributions of this family, we obtain the exact form of Shannon entropy, some of the information properties, and entropy bounds for concomitants of order statistics. Some comparisons are also made between the entropy of order statistics X _(r) and the entropy of its concomitants Y _[r]. In this family, we show that the mutual information between X _(r) and Y _[r], and Kullback–Leibler distance among the concomitants of order statistics are all distribution-free. Also, we compare the Pearson correlation coefficient between X _(r) and Y _[r] with the mutual information of (X _(r), Y _[r]) for the copula model of FGM family.     

Robust variable selection for the varying coefficient model based on composite L 1–L 2 regression

The varying coefficient model (VCM) is an important generalization of the linear regression model and many existing estimation procedures for VCM were built on L ₂ loss, which is popular for its mathematical beauty but is not robust to non-normal errors and outliers. In this paper, we address the problem of both robustness and efficiency of estimation and variable selection procedure based on the convex combined loss of L ₁ and L ₂ instead of only quadratic loss for VCM. By using local linear modeling method, the asymptotic normality of estimation is driven and a useful selection method is proposed for the weight of composite L ₁ and L ₂. Then the variable selection procedure is given by combining local kernel smoothing with adaptive group LASSO. With appropriate selection of tuning parameters by Bayesian information criterion (BIC) the theoretical properties of the new procedure, including consistency in variable selection and the oracle property in estimation, are established. The finite sample performance of the new method is investigated through simulation studies and the analysis of body fat data. Numerical studies show that the new method is better than or at least as well as the least square-based method in terms of both robustness and efficiency for variable selection.     

Karhunen–Loève expansions of Lévy processes

We derive the basis functions and joint distribution of the stochastic coefficients of the Karhunen–Loève expansion of a square-integrable Lévy process. Further, we demonstrate a method for simulating the coefficients via a shot-noise representation.     

L8(4×24)型正交试验表数据处理模型的应用

本文利用Excel和数理统计基础知识对L8(4×24)型混合水平正交试验的数据进行了优化处理。     

Estimation of P(X>Y) with Topp–Leone distribution

We consider the estimation problem of the probability P=P(X>Y) for the standard Topp–Leone distribution. After discussing the maximum likelihood and uniformly minimum variance unbiased estimation procedures for the problem on both complete and left censored samples, we perform a Monte Carlo simulation to compare the estimators based on the mean square error criteria. We also consider the interval estimation of P.