THE SUPERIORITY OF EMPIRICAL BAYES ESTIMATION OF PARAMETERS IN PARTITIONED NORMAL LINEAR MODEL

In this article,the empirical Bayes（EB）estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares（LS）estimator are investigated under mean square error matrix（MSEM）criterion.

EMPIRICAL BAYES TEST PROBLEMS OF VARIANCE COMPONENTS IN RANDOM EFFECTS MODEL

Bayes decision rule of variance components for one-way random effects model is derived and empirical Bayes (EB) decision rules are constructed by kernel estimation method. Under suitable conditions, it is shown that the proposed EB decision rules are asymptotically optimal with convergence rates near O(n-1/2). Finally, an example concerning the main result is given.

One-sided empirical Bayes test for location parameter in Gamma distribution

In this paper, we devote to constructing the one-sided empirical Bayes(EB) test for the location parameter in the Gamma distribution by nonparametric method. Under some mild conditions, we prove that the EB test is asymptotically optimal with the rate of the order O(n^(-δs/(2s+1))), where 1/2 ≤ δ < 1 and s > 1 is a given natural number. An example is also given to illustrate that the conditions of the main theorems are easily satisfied.

Empirical Bayes Test for the Parameter of Rayleigh Distribution with Error of Measurement

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.

Empirical Bayes Test for Two-parameter Exponential Distribution under Type-Ⅱ Censored Samples

The empirical Bayes test problem is considered for scale parameter of twoparameter exponential distribution under type-II censored data.By using wavelets estimation method,the EB test function is constructed,of which the asymptotic optimality and convergence rates are obtained.Finally,an example concerning the main result is given.

Convergence Rate of Empirical Bayes for Two-parameter Exponential Distribution with Replicated Data

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.

Monotone Empirical Bayes Test for the Exponential Distribution

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 improves the existing results in the literature.

Empirical Bayes Prediction in Exponential Distribution

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.

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

Regularized system identification has become the research frontier of system identification in the past decade.One related core subject is to study the convergence properties of various hyper-parameter estimators as the sample size goes to infinity.In 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 given.However,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 required.In general,the convergence in distribution of a sequence of random variables does not necessarily guarantee the convergence of its covariance matrix.Thus,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 estimator.In 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 distribution.Moreover,we run numerical simulations to demonstrate the efficacy of ourtheoretical results.

EMPIRICAL BAYES ESTIMATION FOR ESTIMABLE FUNCTION OF REGRESSION COEFFICIENT IN A MULTIPLE LINEAR REGRESSION MODEL

In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard normal distribution. We get the EB estimators by using kernel estimation of multivariate density function and its first order partial derivatives. It is shown that the convergence rates of the EB estimators are under the condition where an integer k > 1 . is an arbitrary small number and m is the dimension of the vector Y.

Two-Sided Empirical Bayes Test for the Exponential Family with Contaminated Data

In this study, the two-sided Empirical Bayes test （EBT） rules for the parameter of continuous one-parameter exponential family with contaminated data （errors in variables） are constructed by a deconvolution kernel method. The asymptotically optimal uniformly over a class of prior distributions and uniform rates of convergence, which depends on two types of the error distribu- tions for the proposed EBT rules, are obtained under suitable con- ditions. Finally, an example about the main results of this paper is given.

ASYMPTOTICALLY OPTIMAL EMPIRICAL BAYES ESTIMATION FOR THE PARAMETERS OF MULTI－PARAMETER DISCRETE EXPONENTIAL FAMILY

For the multi-parameter discrete exponential family,we construct an empirical Bayes(EB)estimator of the vector-valued parameterθ.under some conditions,this estimator is proved to be asymptotically optimal.

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

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 crossing.The 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 crossbucks.The proposed methodology also accounts for the observed accident count at a crossing using the Empirical Bayes method.The ZINDOT model estimates were compared to the USDOT model estimates to rank the crossings based on the expected accident frequency.It 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 formula.This methodology could be used to rank highway-rail grade crossings for resource allocation and safety improvement.

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

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.