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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

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

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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

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

Assessing quality of crash modification factors estimated by empirical bayes before-after methods

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Journal of Central South University 2020年第8期27卷 2259-2268页

作者： CHEN Ying WU Ling-tao HUANG Zhong-xiang School of Traffic and Transportation Engineering Changsha University of Science&TechnologyChangsha 410114China School of Architecture Changsha University of Science&TechnologyChangsha 410114China Center for Transportation Safety Texas A&M Transportation InstituteBryanTexas77847USA

Before-after study with the empirical bayes(EB)method is the state-of-the-art approach for estimating crash modification factors(CMFs).The EB method not only addresses the regression-to-the-mean bias,but also improves ***,the performance of the CMFs derived from the EB method has never been fully *** study aims to examine the accuracy of CMFs estimated with the EB *** realistic data(ARD)and real crash data are used to evaluate the *** results indicate that:1)The CMFs derived from the EB before-after method are nearly the same as the true values.2)The estimated CMF standard errors do not reflect the true *** estimation remains at the same level regardless of the pre-assumed CMF standard *** EB before-after study is not sensitive to the variation of CMF among sites.3)The analyses with real-world traffic and crash data with a dummy treatment indicate that the EB method tends to underestimate the standard error of the *** researchers should recognize that the CMF variance may be biased when evaluating safety effectiveness by the EB *** is necessary to revisit the algorithm for estimating CMF variance with the EB method.

关键词： traffic safety empirical bayes crash modification factor safety effectiveness evaluation

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

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

A fiducial approach to the nonparametric deconvolution problem:The discrete case

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Science China Mathematics 2024年第11期67卷 2653-2670页

作者： Yifan Cui Jan Hannig Center for Data Science Zhejiang UniversityHangzhou 310058China Department of Statistics and Operations Research University of North Carolina at Chapel HillChapel HillNC 27599USA

Fiducial inference is applied to nonparametric g-modeling in the discrete *** propose a computationally efficient algorithm to sample from the fiducial distribution and use the generated samples to construct point estimates and confidence *** study the theoretical properties of the fiducial distribution and perform extensive simulations in various *** proposed approach gives rise to good statistical performance in terms of the mean squared error of point estimators and coverage of confidence ***,we apply the proposed fiducial method to estimate the probability of each satellite site being malignant using gastric adenocarcinoma data with 844 patients.

关键词： confidence intervals empirical bayes fiducial inference nonparametric deconvolution

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

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