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Moment Selection and Generalized Empirical Likelihood Estimation in High-Dimensional Unconditional Moment Conditions

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Journal of Systems Science & Complexity 2024年第6期37卷 2738-2770页

作者： WANG Wenjun YANG Zhihuang Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan UniversityKunming 650091China

This paper investigates the moment selection and parameter estimation problem of highdimensional unconditional moment conditions. First, the authors propose a Fantope projection and selection(FPS) approach to distinguish the informative and uninformative moments in high-dimensional unconditional moment conditions. Second, for the selected unconditional moment conditions, the authors present a generalized empirical likelihood(GEL) approach to estimate unknown parameters. The proposed method is computationally feasible, and can efficiently avoid the well-known ill-posed problem of GEL approach in the analysis of high-dimensional unconditional moment conditions. Under some regularity conditions, the authors show the consistency of the selected moment conditions, the consistency and asymptotic normality of the proposed GEL estimator. Two simulation studies are conducted to investigate the finite sample performance of the proposed methodologies. The proposed method is illustrated by a real example.

关键词： Fantope projection and selection generalized empirical likelihood high dimensionality moment selection unconditional moment condition

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Diagnostic Measures for Functional Linear Model with Nonignorable Missing Responses

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Communications in Mathematics and Statistics 2024年第3期12卷 543-562页

作者： Yujian Zhu Puying Zhao Key Lab of Statistical Modeling and Data Analysis of Yunnan Province Yunnan UniversityKunmingPeople’s Republic of China

Assessing the influence of individual observations of the functional linear models is important and challenging,especially when the observations are subject to *** this paper,we introduce three case-deletion diagnostic measures to identify influential observations in functional linear models when the covariate is functional and observations on the scalar response are subject to nonignorable *** nonignorable missing data mechanism is modeled via an exponential tilting semiparametric functional model.A semiparametric imputation procedure is developed to mitigate the effects of missing *** estimations of the functional coefficients are based on functional principal components analysis using the imputed dataset.A smoothed bootstrap samplingmethod is introduced to estimate the diagnostic probability for each proposed diagnostic measure,which is helpful to unveil which observations have the larger influence on estimation and *** studies and a real data example are conducted to illustrate the finite performance of the proposed methods.

关键词： Case deletion Diagnostic measure Functional linear model Nonignorable nonresponse Semiparametric imputation

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Variational Bayesian Tensor Quantile Regression

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Acta Mathematica Sinica,English Series 2025年第2期41卷 733-756页

作者： Yunzhi Jin Yanqing Zhang Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan UniversityKunming 650091P.R.China Yunnan Key Laboratory of Statistical Modeling and Data Analysis Southwest United Graduate SchoolYunnan UniversityKunming 650091P.R.China

Quantile regression is widely used in variable relationship research for statistical *** quantile regression model is based on vector-valued covariates and can be efficiently estimated via traditional estimation ***,many modern applications involve tensor data with the intrinsic tensor *** quantile regression can not deal with tensor regression issues *** this end,we consider a tensor quantile regression with tensor-valued covariates and develop a novel variational Bayesian estimation approach to make estimation and prediction based on the asymmetric Laplace model and the CANDECOMP/PARAFAC decomposition of tensor *** incorporate the sparsity of tensor coefficients,we consider the multiway shrinkage priors for marginal factor vectors of tensor *** key idea of the proposed method is to efficiently combine the prior structural information of tensor and utilize the matricization of tensor decomposition to simplify the complexity of tensor coefficient *** coordinate ascent algorithm is employed to optimize variational lower *** studies and a real example show the numerical performances of the proposed method.

关键词： Asymmetric Laplace model CANDECOMP PARAFAC decomposition matricization tensor quantile regression variational Bayesian

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Feedback of Efficient Shock Acceleration on Magnetic-field Structure Inside Young Type Ia Supernova Remnants

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Research in Astronomy and Astrophysics 2024年第6期24卷 234-244页

作者： Jun-Yu Shen Bi-Wen Bao Li Zhang Department of Astronomy Key Laboratory of Astroparticle Physics of Yunnan ProvinceYunnan UniversityKunming 650091China Key Laboratory of Statistical Modeling and Data Analysis of Yunnan Province Yunnan UniversityKunming 650091China

Using an effective adiabatic index γ_(eff) to mimic the feedback of efficient shock acceleration,we simulate the temporal evolution of a young type Ia supernova remnant (SNR) with two different background magnetic field(BMF) topologies:a uniform and a turbulent *** density distribution and magnetic-field characteristics of our benchmark SNR are studied with two-dimensional cylindrical magnetohydrodynamic *** γ_(eff)is considered,we find that:(1) the two-shock structure shrinks and the downstream magnetic-field orientation is dominated by the Rayleigh–Taylor instability structures;(2) there exists more quasi-radial magnetic fields inside the shocked region;and (3) inside the intershock region,both the quasi-radial magnetic energy density and the total magnetic energy density are enhanced:in the radial direction,with γ_(eff)=1.1,they are amplified about 10–26 times more than those with γ_(eff)=5/*** in the angular direction,the total magnetic energy densities could be amplified about 350 times more than those with γ_(eff)=5/3,and there are more grid cells within the intershock region where the magnetic energy density is amplified by a factor greater than 100.

关键词： methods:numerical ISM:magnetic fields ISM:supernova remnants magnetohydrodynamics(MHD)

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Efficient Estimation of Single-index Models with Deep ReQU Neural Networks

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Acta Mathematica Sinica,English Series 2025年第2期41卷 640-676页

作者： Zhihuang Yang Siming Zheng Niansheng Tang Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan UniversityKunming 650091P.R.China School of Medicine Yale UniversityNew HavenCT 06520USA

Single-index model offers the greater flexibility of modelling than generalized linear models and also retains the interpretability of the model to some extent. Although many standard approaches such as kernels or penalized/smooothing splines were proposed to estimate smooth link function, they cannot approximate complicated unknown link functions together with the corresponding derivatives effectively due to their poor approximation ability for a finite sample size. To alleviate this problem, this paper proposes a semiparametric least squares estimation approach for a single-index model using the rectifier quadratic unit (ReQU) activated deep neural networks, called deep semiparametric least squares (DSLS) estimation method. Under some regularity conditions, we show non-asymptotic properties of the proposed DSLS estimator, and evidence that the index coefficient estimator can achieve the semiparametric efficiency. In particular, we obtain the consistency and the convergence rate of the proposed DSLS estimator when response variable is conditionally sub-exponential. This is an attempt to incorporate deep learning technique into semiparametrically efficient estimation in a single index model. Several simulation studies and a real example data analysis are conducted to illustrate the proposed DSLS estimator.

关键词： Asymptotical normality deep neural networks non-asymptotic estimation error bound semiparametric efficiency single-index models

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Least Square Estimation for Multiple Functional Linear Model with Autoregressive Errors

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Acta Mathematicae Applicatae Sinica 2025年第1期41卷 84-98页

作者： Meng WANG Ming-liang SHU Jian-jun ZHOU Si-xin WU Min CHEN School of Management University of Science and Technology of ChinaHefei 230026China Academy of Mathematics and System Science Chinese Academy of SciencesBeijing 100190China Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan UniversityKunming 650091China

As an extension of linear regression in functional data analysis, functional linear regression has been studied by many researchers and applied in various fields. However, in many cases, data is collected sequentially over time, for example the financial series, so it is necessary to consider the autocorrelated structure of errors in functional regression background. To this end, this paper considers a multiple functional linear model with autoregressive errors. Based on the functional principal component analysis, we apply the least square procedure to estimate the functional coefficients and autoregression coefficients. Under some regular conditions, we establish the asymptotic properties of the proposed estimators. A simulation study is conducted to investigate the finite sample performance of our estimators. A real example on China's weather data is applied to illustrate the validity of our model.

关键词： multiple functional linear model autoregressive errors principal component analysis consistency

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Estimation of Treatment Effects in Nonlinear Models with Unobserved Confounding

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Acta Mathematicae Applicatae Sinica 2023年第2期39卷 320-336页

作者： Yu-ling LI Jun WANG Research Center for Applied Mathematics and Interdisciplinary Sciences Beijing Normal UniversityZhuhai 519087China Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan UniversityKunming 650091China

Estimation of treatment effects is one of the crucial mainstays in economics and sociology *** problem will become more serious and complicated if the treatment variable is endogenous for the presence of unobserved *** estimation and conclusion are likely to be biased and misleading if the endogeny of treatment variable is *** this article,we propose the pseudo maximum likelihood method to estimate treatment effects in nonlinear *** proposed method allows the unobserved confounding and random error terms to exist in an arbitrary relationship(such as,add or multiply),and the unobserved confounding have different influence directions on treatment variables and outcome *** proposed estimator is consistent and asymptotically normally *** studies show that the proposed estimator performs better than the special regression estimator,and the proposed method is stable for various distribution of error ***,the proposed method is applied to the real data that studies the influence of individuals have health insurance on an individual’s decision to visit a doctor.

关键词： nonlinear models quasi likelihood estimator stable treatment effects unobserved confounding

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Adaptive Subspace Detection of Range-Distributed Targets in Compound Gaussian Clutter with Generalized Inverse Gaussian Texture 2

Adaptive Subspace Detection of Range-Distributed Targets in ...

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2nd IEEE International Conference on Signal, Information and data Processing, ICSIDP 2024

作者： Wang, Xin Rong, Yao Tang, Mengjiao Li, Fan Hao, Chenchen Yunnan University Yunnan Key Laboratory of Statistical Modeling and Data Analysis Kunming China University of China Key Laboratory of Flight Techniques and Flight Safety Civil Aviation Flight Guanghan China

ISBN: (纸本)9798331515669

This paper addresses adaptive subspace detection of range-distributed targets in compound Gaussian clutter with Generalized Inverse Gaussian (GIG) texture. Novel adaptive subspace detectors are developed based on the generalized likelihood ratio, Rao, and Wald test criteria, employing two-step design strategies that incorporate the persymmetric covariance structure and the GIG texture distribution to enhance detection performance. Furthermore, to achieve full adaptivity, a novel method is proposed for adaptively estimating the clutter texture parameters. The effectiveness of the proposed adaptive detectors, combined with this new texture parameter estimation method, is validated via numerical examples in various non-Gaussian clutter environments, demonstrating superior detection performance compared to several existing methods. © 2024 IEEE.

关键词： Clutter (information theory)

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Adaptive Radar Detection in Compound-Gaussian Environments with Missing data 2

Adaptive Radar Detection in Compound-Gaussian Environments w...

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2nd IEEE International Conference on Signal, Information and data Processing, ICSIDP 2024

作者： Hao, Chenchen Rong, Yao Tang, Mengjiao Li, Fan Wang, Xin Yunnan University Yunnan Key Laboratory of Statistical Modeling and Data Analysis Kunming China Civil Aviation Flight University of China Key Laboratory of Flight Techniques and Flight Safety Guanghan China

ISBN: (纸本)9798331515669

This paper addresses adaptive radar detection in scenarios with incomplete observations due to measurement errors, sensor failures, or outliers, where the target is embedded in compound Gaussian clutter with unknown covariance matrix. The detection problem is formulated as a binary hypothesis test, with a set of selection matrices introduced to represent the observations at each snapshot. At the stage of detector design, a two-step design strategy is employed: first, the Generalized Likelihood Ratio Test (GLRT) is derived assuming known covariance structure;then, the actual covariance matrix in the GLRT is replaced with its maximum likelihood estimate, which is calculated based on the non-missing components of the secondary data using an expectation-maximization (EM) algorithm developed in this paper. Numerical examples demonstrate the effectiveness of these detectors in compound Gaussian clutter environments, showing superior performance compared to the existing detector designed for scenarios with Gaussian interference and missing data, as well as the classical linear imputation method. © 2024 IEEE.

关键词： Expectation maximization algorithm

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Estimation of the Number of Signals in White Noise via Large-Sample and High-Dimensional Asymptotic Theory 22

Estimation of the Number of Signals in White Noise via Large...

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22nd IEEE International Conference on Communication Technology, ICCT 2022

作者： Rong, Yao Zhang, Lewen Tang, Mengjiao Zan, Zeqiong Yunnan University Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan Kunming650504 China

ISBN: (纸本)9781665470674

This paper focuses on estimating the number of source signals embedded in Gaussian white noise. We address this problem via a sequence of nested hypothesis tests, and construct variance statistics based on eigenvalues of the sample covariance for each candidate hypothesis. Then, a detailed statistical analysis of these statistics is carried out in both the large-sample and high-dimensional regimes. According to this analysis, we propose a new scheme for determining the number of source signals in both the sample-rich and sample-starved cases. Finally, numerical examples are presented to show its superiority compared to some existing estimation methods. © 2022 IEEE.

关键词： Eigenvalues and eigenfunctions

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