基于众数回归的变系数部分非线性模型的稳健估计

针对变系数部分非线性模型,提出了一种稳健的基于众数回归的两阶段估计方法.首先,基于B-样条函数近似系数函数,利用QR正交分解技术构造了非线性模型,得到了参数的非线性最小二乘估计.其次,提出了变系数函数的众数回归估计量.在一定条件下,证明了估计量的渐近性质.通过数值模拟和实际数据分析,说明了所提估计方法的有效性.     

缺失数据下基于众数回归的变系数部分非线性模型的估计

针对响应变量随机缺失的变系数部分非线性模型,提出了一种稳健的基于众数回归的估计方法.采取逆概率加权方法,利用QR正交分解技术,分别得到了未知参数和变系数函数的众数回归估计量.在一定条件下,证明了估计量的渐近性质.通过数值模拟和实际数据分析,说明了所提估计方法的有效性.     

单指标众数模型的统计诊断及在波士顿房价分析中的应用

在金融、经济、社会科学、气候科学、环境科学、工程技术和生物医学等领域,数据分布常常呈现出尖峰厚尾的特征,且密度分布是不对称的有偏分布。此时,单指标众数模型是刻画这些特征的一个重要方法。为此,非常有必要研究该模型下的统计诊断。本文将考虑单指标众数模型基于数据删除模型和众数漂移模型的统计诊断与局部影响分析。模拟研究和波士顿房价数据的结果表明所提出的方法是有效和可行的。     

协变量缺失情形下的逆概率加权众数回归估计

数据缺失在实际应用中普遍存在,数据缺失会降低研究效率,导致参数估计有偏.在协变量随机缺失(MAR)的假定下,本文基于众数回归和逆概率加权估计方法对线性模型进行参数估计.该方法结合参数Logistic回归和非参数Nadaraya-Watson估计两种倾向得分估计方法,分别构建IPWM-L估计量和IPWM-NW估计量.模拟研究和实例分析表明,众数回归模型比均值回归模型更具稳健性,逆概率加权众数(IPWM)估计方法在缺失数据下表现出了更好的拟合效果,与IPWM-L估计量相比, IPWM-NW估计量更稳健.     

基于众数回归的变系数部分线性工具变量模型的稳健估计

基于众数回归,利用工具变量研究含有内生变量的变系数部分线性模型的稳健估计.首先,引入工具变量对内生协变量进行分解,从而得到内生协变量的一致估计;其次,运用B样条基函数近似模型中的非参数部分,将模型简化;进一步,基于众数回归的思想,结合EM算法得到参数和非参数函数的估计.在一定条件下,证明估计量的大样本性质;最后,利用模拟实验和真实实例验证所提方法的有效性.     

长方体上均匀分布的密度函数

讨论了长方体上均匀分布密度函数问题,得到了长方体体积的估计量、估计量的点估计及估计量的密度函数.     

配对数据条件得分函数:Mantel-Haenszel估计量推广

提出配对数据条件得分函数,用其推广Mantel-Haenszel估计量;给出指数分布族模型下推广的Mantel-Haenszel型估计量表达式或估计方程,解释估计量具有稳健性的原因,并给出应用实例。     

基于众数回归的部分函数型线性可加模型的稳健估计

本文讨论部分函数型线性可加模型参数的稳健估计,该模型由经典的可加回归模型和函数型线性模型组合而成.采用B-样条基函数对模型中斜率函数和非参数可加函数进行近似,然后通过最大化众数回归目标函数得到基于众数回归的估计.在一些正则条件下,本文给出估计的收敛速度和渐近分布.最后通过模拟计算和应用实例以表明所提方法的有效性.模拟结果表明,该方法不仅具有稳健性,即不易受污染数据或厚尾分布的影响,而且在信噪比较大时可以与最小二乘方法有相同的表现.     

带跳单指标模型的半参数跳点检测估计

单指标模型是统计学中常用的维数约减模型.在实际应用中,连接函数可能有奇异点,包括某些未知位置上有跳点和某些相关过程的结构变点.检测这些奇异点对于系数估计和了解结构改变非常重要.本文基于精细最小平均条件方差估计和函数二阶导数的零穿越性质,提出一个跳点检测方法,然后利用检测出的跳点给出参数向量和连接函数的半参数跳点检测估计量,并讨论程序参数的选择.在较弱的假设条件下,本文建立跳点检测程序和所提估计量的大样本性质.数值模拟和实例分析验证了所提方法在有限样本下的表现.     

非参数模型的稳健跳点检测估计

非参数模型是统计学中常用的一类模型.在实际应用中,回归函数可能不是连续的,即在某些未知的位置上存在跳点.检测这些跳点对于回归函数的估计非常重要.本文基于B样条和众数估计,提出一个稳健跳点检测方法.然后利用检测出的跳点给出了回归函数的稳健有效估计量,并讨论了参数的选择.数值模拟和实例分析验证了所提方法在有限样本下的表现.     

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.