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On convergence of covariance matrix of empirical bayes hyper-parameter estimator

Control Theory and Technology 2024年第2期22卷 149-162页

作者： Yue Ju Biqiang Mu Tianshi Chen School of Data Science and Shenzhen Research Institute of Big Data The Chinese University of Hong KongShenzhenShenzhen518172GuangdongChina Division of Decision and Control Systems School of Electrical Engineering and Computer ScienceKTH Royal Institute of Technology10044StockholmSweden Key Laboratory of Systems and Control Institute of Systems ScienceAcademy of Mathematics and System ScienceChinese Academy of SciencesBeijing100190China

Regularized system identification has become the research frontier of system identification in the past *** related core subject is to study the convergence properties of various hyper-parameter estimators as the sample size goes to *** this paper,we consider one commonly used hyper-parameter estimator,the empirical bayes(EB).Its convergence in distribution has been studied,and the explicit expression of the covariance matrix of its limiting distribution has been ***,what we are truly interested in are factors contained in the covariance matrix of the EB hyper-parameter estimator,and then,the convergence of its covariance matrix to that of its limiting distribution is *** general,the convergence in distribution of a sequence of random variables does not necessarily guarantee the convergence of its covariance ***,the derivation of such convergence is a necessary complement to our theoretical analysis about factors that influence the convergence properties of the EB hyper-parameter *** this paper,we consider the regularized finite impulse response(FIR)model estimation with deterministic inputs,and show that the covariance matrix of the EB hyper-parameter estimator converges to that of its limiting ***,we run numerical simulations to demonstrate the efficacy of ourtheoretical results.

关键词： Regularized system identification Hyper-parameter estimator empirical bayes Convergence of covariance matrix

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empirical bayes Estimation in Regression Model

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Acta Mathematicae Applicatae Sinica 2005年第4期21卷 537-544页

作者： Li-chun Wang Department of Mathematics School of Sciences Beijing Jiaotong University Beijing 100044 China

This paper considers the empirical bayes （EB） estimation problem for the parameter β of the linear regression model y = Xβ＋ ε with ε- N（0, σ^2I） given β. Based on Pitman closeness （PC） criterion and mean square error matrix （MSEM） criterion, we prove the superiority of the EB estimator over the ordinary least square estimator （OLSE）.

关键词： Linear regression empirical bayes PC criterion MSEM criterion

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empirical bayes Test for the Parameter of Rayleigh Distribution with Error of Measurement

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Communications in Mathematical Research 2011年第1期27卷 17-23页

作者： HUANG JUAN School of Science Guangdong Ocean University Zhanjiang Guangdong 521088

For the data with error of measurement in historical samples, the empirical bayes test rule for the parameter of Rayleigh distribution is constructed, and the asymptotically optimal property is obtained. It is shown that the convergence rate of the proposed EB test rule can be arbitrarily close to O（n-1/2） under suitable conditions.

关键词： error of measurement empirical bayes asymptotic optimality convergence rate

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empirical bayes Prediction in Exponential Distribution

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Northeastern Mathematical Journal 2005年第3期21卷 329-335页

作者：王立春 institute of Applied Mathematics AMSSCASBeijing100080

This paper concerns with an empirical bayes prediction problem in exponential distribution. Using observed samples, we construct a prediction interval for a set of interest which consists of some unobserved samples. Simulation studies with different prior distributions are conducted to examine coverage probability of the prediction interval.

关键词： empirical bayes prediction confidence interval

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Convergence Rate of empirical bayes for Two-parameter Exponential Distribution with Replicated Data

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Communications in Mathematical Research 2010年第3期26卷 211-218页

作者： Wang De-hui LI NAI-YI 不详 Faculty of Science Guangdong Ocean University Zhanjiang Guangdong 524088

In this paper, empirical bayes test for a parameter θ of two-parameter exponential distribution is investigated with replicated past data. Under some conditions, the asymptotically optimal property is obtained. It is indicated that the rate of convergence can be very close to O（N-2^-1） in this case that a parameter μ is known.

关键词： replicated data empirical bayes asymptotic optimality

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Monotone empirical bayes Test for the Exponential Distribution

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Northeastern Mathematical Journal 2006年第3期22卷 265-274页

作者：王立春 Institute of Applied Mathematics Chinese Academy of Sciences

We study the two-action problem in the exponential distribution via empirical bayes （EB） approach. Based on type Ⅱ censored samples, we construct an EB test rule and obtain an optimal rate of convergence which much... 详细信息

关键词： empirical bayes exponential distribution rate of convergence

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Safety effectiveness of roadway conversion with a two way left turn lane

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Journal of Traffic and Transportation Engineering(English Edition) 2018年第4期5卷 309-317页

作者： Subasish Das Xiaoduan Sun Karen Dixon M.Ashifur Rahman Texas A&M Transportation Institute Texas A&M University College Station Department of Civil Engineering University of Louisiana at Lafayette

In urban or suburban areas with a large number of access points, four-lane undivided highways are prone to crashes due to left-turning and through movements in a single lane. Many studies recommended expensive countermeasures like conversion from undivided to divided road with physical separation. One inexpensive alternative is reconfiguring the existing roadways by either increasing or decreasing the number of lanes. This study investigated the safety impact of converting four lane undivided roadways （4U） to five lane undivided roadways （ST） with a two way left turn lane （TIkrLTL）. This study used empirical bayes method to determine the safety impact of this inexpensive countermeasure. In this study, data from eight sites from Louisiana were collected for investigation, and site- specific crash modification factor （CMF） values were calculated. Although ST is usually not preferable due to its exposure of higher number of crashes in the existing literature, the findings of the current study indicated a positive safety impact. The benefit-cost ratio of this conversion ranges from 97 to 379. The current findings indicate that conversion of 4U to 5T is a feasible inexpensive solution for urban roadways with lower volume and a limited number of driveways.

关键词： Lane restriping Two way left turn lane empirical bayes Crash modification factor Benefit cost ratio

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Multi-locus GWAS and linkage analysis for mapping small and linked QTLs

Multi-locus GWAS and linkage analysis for mapping small and ...

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2018中国作物学会学术年会

作者：章元明 Crop Information Center College of Plant Science and TechnologyHuazhong Agricultural University

Genome-wide association studies(GWAS) have been widely used in genetic dissection of complex ***,common methods are almost based on single-marker genome scanning under the framework of mixed linear model(MLM) with population structure and polygenic background *** methods require Bonferroni correction for multiple tests,which often is too conservative to detect some important loci for complex traits when the number of markers is extremely large,especially for relatively large error in the measurement of phenotypic values in crop field *** address this issue,we proposed a series of methods for multi-locus genome-wide association study(GWAS),including mrMLM,FASTmrMLM,FASTmrEMMA,ISIS EM-BLASSO,pLARmEB and *** the methods are built on random SNP effect and new ***,various algorithms are used to scan each marker on the genome or all the markers on each chromosome or the whole genome to find all the markers that are potentially associated with the *** these algorithms,FASTmrEMMA whitens the covariance matrix of the polygenic matrix K and environmental noise,this algorithm is integrated with LAR algorithm and non-parameteric test to develop pLARmEB and pKWmEB,respectively,and FASTmrMLM is the integration of mrMLM with GEMMA and ***,all the selected markers are placed into one model,their effects are estimated by empirical bayes,and all the non-zero effects are identified for true QTNs by a likelihood ratio *** generalize the above methods,these methods were integrated into an R software *** v3.1,which includes dataset input,parameter setting and result output(https://***/web/packages/***/***).The fread function in *** is used to quickly read datasets,especially for big datasets;doParallel package is used to conduct parallel computation using multiple *** validate the software,the same simulation datasets in previous studies were re-analyzed by all the me

关键词： genome-wide association studies mixed linear model multi-locus model genome-wide composite interval mapping empirical bayes R

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On SURE-Type Shrinkage Estimation

On SURE-Type Shrinkage Estimation

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第十届海峡两岸统计与概率研讨会

作者： Zhouping LI Lanzhou University

The talk is concerned with empirical bayes shrinkage estimators for the heteroscedastic hierarchical normal model using Stein’s unbiased estimate of risk(SURE). Xie, et al.(2012) studied this problem assuming known but unequal variances. In this paper, we consider this problem with unequal and unknown variances, which may be more appropriate in real situations. By placing priors for both means and variances, we propose novel SURE-type double-shrinkage estimators which shrink both means and variances. Optimal properties for these estimators are derived under certain regularity conditions. Simulations are conducted to compare the new methods with other shrinkage techniques, and it is also applied to the well-known baseball data set and a gene expression data set.

关键词： empirical bayes SURE Double shrinkage

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A New Accident Prediction Model for Highway-Rail Grade Crossings Using the USDOT Formula Variables

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Journal of Traffic and Transportation Engineering 2020年第1期8卷 1-13页

作者： Jacob Mathew Rahim F Benekohal Civil and Environmental Engineering University of Illinois Urbana-ChampaignNewmark Civil Engineering Building205 N.Mathews AveUrbana 61801IllinoisUSA

This paper presents the ZINDOT model,a methodology utilizing a zero-inflated negative binomial model with the variables used in the United States Department of Transportation(USDOT)accident prediction formula,to determine the expected accident count at a highway-rail grade *** model developed contains separate formulas to estimate the crash prediction value depending on the warning device type installed at the crossing:crossings with gates,crossings with flashing lights and no gates,and crossings with *** proposed methodology also accounts for the observed accident count at a crossing using the empirical bayes *** ZINDOT model estimates were compared to the USDOT model estimates to rank the crossings based on the expected accident *** is observed that the new model can identify crossings with a greater number of accidents with Gates and Flashing Lights and Crossbucks in both Illinois(data which were used to develop the model)and Texas(data which were used to validate the model).A practitioner already using the USDOT formulae to estimate expected accident count at a crossing could easily use the ZINDOT model as it employs the same variables used in the USDOT *** methodology could be used to rank highway-rail grade crossings for resource allocation and safety improvement.

关键词： Highway-rail grade crossing accident prediction USDOT formulae zero inflated negative binomial empirical bayes

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