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BOUNDS ON AVERAGE CONTROLLED DIRECT EFFECTS WITH AN UNOBSERVED RESPONSE VARIABLE

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Journal of Systems Science & Complexity 2011年第6期24卷 1154-1164页

作者： Na SHAN jianhua guo Key Laboratory for Applied statistics of Ministry of Education School of Mathematics and Statistics Northeast Normal University Changchun 130024 China school of Basic Science Changchun University of Technology Changchun 130012 China

This paper considers the problem of estimating the bounds on the average controlled direct effects （ACDEs） of a treatment variable on an unobserved response variable in the presence of unobserved confounders between an intermediate variable and the response variable. When the response variable is observed, Cai, et al.（2008） derived the formulas for the sharp bounds on the ACDEs. When the response variable is unobserved, the authors propose a graphical criterion for selecting variables affected by the response variable to derive the formulas for the bounds on the ACDEs, which is an extension of the result of Kuroki（2005） to ACDEs. The results enable us not only to judge from the graph structure whether the bounds on the ACDEs can be expressed through observed variables when the response variable is unobserved, but also to provide their formulas when the answer is affirmative.

关键词： Average controlled direct effect causal network d-separation

Decomposition of two classes of structural models

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Frontiers of mathematics in China 2013年第6期8卷 1323-1349页

作者： Benchong LI jianhua guo Key Laboratory for Applied statistics of MOE and school of mathematics and statistics Northeast Normal University Changchun 130024 China

The conditional independence structure of a common probability measure is a structural model. In this paper, we solve an open problem posed by Studeny [Probabilistic Conditional Independence Structures, Theme 9, p. 206]. A new approach is proposed to decompose a directed acyclic graph and its optimal properties are studied. We interpret this approach from the perspective of the decomposition of the corresponding conditional independence model and provide an algorithm for identifying the maximal prime subgraphs in a directed acyclic graph.

关键词： Combinatorial imset conditional independence model decomposition directed acyclic graph undirected graph

A likelihood-based method for haplotype association studies of case-control data with genotyping uncertainty

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Science China mathematics 2006年第1期49卷 130-144页

作者： ZHU Wensheng guo jianhua school of mathematics and statistics Northeast Normal University Changchun 130024 China School of Mathematics and Statistics Northeast Normal University Changchun 130024 China

This paper discusses the associations between traits and haplotypes based on Fl (fluorescent intensity) data sets, We consider a clustering algorithm based on mixtures of t distributions to obtain all possible genotypes of each individual (i.e. "GenoSpectrum"). We then propose a likelihood-based approach that incorporates the genotyping uncertainty to assessing the associations between traits and haplotypes through a haplotypebased logistic regression model, Simulation studies show that our likelihood-based method can reduce the impact induced by genotyping errors.

关键词： haplotype-based association GenoSpectrum case-control study genotyping error logistic regres-

A note on statistical analysis of factor models of high dimension

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Science China mathematics 2021年第8期64卷 1905-1916页

作者： Zhigen Gao jianhua guo Yanyuan Ma KLAS and school of mathematics and statistics Northeast Normal UniversityChangchun 130024China Department of statistics Pennsylvania State UniversityUniversity ParkPA 16802USA

Linear factor models are familiar tools used in many *** pioneering literatures established foundational theoretical results of the quasi-maximum likelihood estimator for high-dimensional linear factor *** results are based on a critical assumption:The error variance estimators are uniformly bounded in *** of making such an assumption,we provide a rigorous proof of this result under some mild conditions.

关键词： bounded in probability heteroscedasticity high-dimensional linear factor model

Decomposition of Covariate-Dependent Graphical Models with Categorical Data

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Communications in Mathematical Research 2023年第3期39卷 414-436页

作者： Binghui Liu jianhua guo school of mathematics and statistics&KLAS Northeast Normal UniversityChangchunJilin 130024P.R.China

Graphical models are wildly used to describe conditional dependence relationships among interacting random *** statistical inference problems of a graphical model,one particular interest is utilizing its interaction structure to reduce model *** an important approach to utilizing structural information,decomposition allows a statistical inference problem to be divided into some sub-problems with lower *** this paper,to investigate decomposition of covariate-dependent graphical models,we propose some useful definitions of decomposition of covariate-dependent graphical models with categorical data in the form of contingency *** on such a decomposition,a covariate-dependent graphical model can be split into some sub-models,and the maximum likelihood estimation of this model can be factorized into the maximum likelihood estimations of the ***,some sufficient and necessary conditions of the proposed definitions of decomposition are studied.

关键词： Collapsibility contingency tables covariate-dependent decomposition graphical models

高中生数学抽象能力发展水平划分与基于水平划分的调查研究

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课程．教材．教法 2022年第6期42卷 124-131页

作者：郭民史宁中朱立明秦德生东北师范大学数学与统计学院长春130024 唐山师范学院教育学院唐山063000

数学抽象能力作为数学关键能力之一,涵盖数量关系与空间图形两个横向维度,可以划分为归纳与释义、关联与构建、拓展与普适三个纵向水平。基于水平划分的调研结果表明:高中生数学抽象能力呈现进阶发展趋势;高中生数学抽象能力在数量关系... 详细信息

数学抽象能力作为数学关键能力之一,涵盖数量关系与空间图形两个横向维度,可以划分为归纳与释义、关联与构建、拓展与普适三个纵向水平。基于水平划分的调研结果表明:高中生数学抽象能力呈现进阶发展趋势;高中生数学抽象能力在数量关系与空间图形上发展不均衡;高三年级学生数学抽象能力的归纳与释义有待提升;高中生数学抽象能力的发展与学生所在年级有关。

关键词：高中生数学抽象能力数学关键能力横向维度纵向水平