批发零售贸易业、餐饮业抽样调查方案及数据处理方法

本文介绍我国批发零售贸易业、餐饮业调查的抽样方案,方案以省为总体,区县为初级抽样单元,为满足对部分地市(域)估计的需要,对区县的抽样考虑了不放回样本追加。文中也给出了与抽样方案配套的总体和域目标量的估计及相应的方差估计公式。     

双无回答层抽样的三重抽样比率估计量

无回答在抽样调查中经常出现,无回答层再抽样是解决无回答的常用方法.当辅助变量总体均值未知时,本文讨论了双无回答层抽样的三重抽样方法,给出了三重抽样的分层汉森-赫维茨估计量和比率估计量,以及它们的方差和估计方差.给出满足事前给定总调查费用约束的三重抽样过程的最优设计参数,以及比率估计量的方差估计.给定总调查成本,三重抽样的分层汉森—赫维茨估计量与比率估计量进行模拟比较,演示比率估计量的优良性.     

Stein两阶段抽样问题中第一阶段最优抽样量研究

当精度和可靠度给定时，Stein（1945）提出了两阶段抽样方法，构造了同时满足一定可靠度与精度的区间估计．本文则利用数值计算方法，进一步给出了此两阶段抽样中最优的第一阶段抽样量．     

二阶抽样总体比率的估计

本文研究二阶抽样下总体比率的估计问题, 就若干种情形给出总体比率的几种可行的估计量,讨论了它们的统计性质.     

长沙市规模以下零售业抽样调查方案

本文介绍了一个根据具体城市情况制定的零售贸易餐饮业的抽样调查方案.以长沙市规模以下零售业、餐饮业为总体,用区域抽样代替一般的名录抽样,并采用细致的分层解决商业单位分布不均匀问题.文中也给出了与抽样方案配套的总体和域目标量的估计及相应的方差估计公式.     

集团抽样不等概方法的均值估计及其性质

在集团抽样调查中，［１］和［２］给出了一般抽样方法及均值估计和它性质的论述，但未考虑各集团在总体中的地位对估计结果的影响．本文给出了集团抽样的不等概方法和均值的无偏估计，同时也给出了这种估计的方差及方差的无偏估计．     

集团抽样不等概方法的均值估计及其性质

在集团抽样调查中，[1]和[2]给出了一般抽样方法及均值估计和它性质的论述，但未考虑各集团在总体中的地位对估计结果的影响，本文给出了集团抽样的不等概方法和均值的无偏估计，同时也给出了这种估计的方差及方差的无偏估计。     

多阶连续抽样设计下广义加权回归估计方法研究

在抽样调查领域中,关于抽样方案设计的研究应用较为充分和完整,但关于抽样估计的研究应用却较为缺乏和滞后。本文首先总结了国外相关研究成果,研究了基于广义加权回归的抽样估计方法,同时证明其满足渐近设计无偏和最小化渐近期望方差的理论条件。同时,本文以各类常见的抽样设计为基础,通过模型组和模型水平将现有的超总体回归模型进行扩展,基于复杂的多阶连续抽样调查,建立各种类型的超总体回归模型进行模型辅助的广义加权回归抽样估计,给出了具体的回归估计步骤和结果,最终形成一套关于广义加权回归抽样估计的理论方法体系,为抽样估计方法在我国政府统计部门中的有效应用奠定理论基础。     

在几种常见的抽样方案下的事后分层

本文给出系统抽样，放回不等概率抽样及二阶不等概率抽样情况下总体均值的事后分层估计，估计量的方差和它的无偏估计。     

多阶等距抽样下总体总值估计量的方差估计

本文给出了多阶抽样下构造总体总值估计量的方差估计量的一种方法．由此，可以得到多阶等距抽样下总体总值估计量的方差估计．     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

Estimates of stability of characterization of additive types of distributions

An estimate of stability of characterization of distribution types is obtained for the case of additive types. Under some conditions, the estimate has the order ε^1/3L(ε), where L(ε) is a slowly varying function. Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I.     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

一类完全正则半群簇子簇格的性质

本文研究了完全正则半群簇的子簇格［Ｖ＋∩ＰＶ，Ｖ＋∩ＰＶ］的某些格运算性质，我们证明了簇Ｖ＋∩ＰＶ可分解为Ｖ与Ｖ＋∩ＰＶ的并；对任意完全正则半群簇Ｗ，有Ｗ∩（Ｖ∨Ｖ＋∩ＰＶ）＝（Ｗ∩Ｖ）∨（Ｗ∩Ｖ＋∩ＰＶ）．特别地，我们得到了等式Ｖ＋∩ＰＶ＝Ｖ成立的若干条件．     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Bases of the identities of products of certain varieties of groups

The following theorem is proved: The product of any variety of two-step solvable groups and a variety having a finite basis of identity relations has a finite basis of identity relations.Translated from Matematicheskie Zametki, Vol. 5, No. 1, pp. 137–144, January, 1969.     

Preservation of equivalence of derivations under reduction of depth of formulas

In this paper we consider derivations in the (&, )-fragment of the intuitionistic propositional calculus. As is known, replacement of any occurrence of a formula [F] in a sequent S by an occurrence of the formula [p], where p is a new propositional variable, with the simultaneous addition to the antecedent of the formula F p or p F depending on the sign of the occurrence of F in S, leaves the derivability unchanged. We give a proof of the fact that the natural extension of this transformation to derivations preserves the relation of equivalence of derivations, i.e., transformed derivations are equivalent if and only if the originals are equivalent. (Derivations are considered equivalent if certain of their normal forms coincide, or, what is the same, if their deductive terms coincide.) It is proved that by the iteration of this transformation, each derivation of an arbitrary sequent S can be transformed into a derivation of a sequent S, depending only on S, whose succedent is a variable, and in the antecedent there occur only formulas of the form a,a & b, a b,,(a b) c, a & b c, a (b & c), wherea, b, c are variables. Here if S is balanced, then S is also balanced. (A sequent is called balanced if each variable occurs in it no more than twice.) The familiar correspondence between certain concepts of the theory of categories and concepts of the theory of proofs allows one to assert that there has been constructed a univalent functor, mapping a free Cartesian closed category into itself.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 88, pp. 197–207, 1979.