Comparison between Empirical Estimation by JRC-JCS Model and Direct Shear Test for Joint Shear Strength

In order to study the reliability of the empirical estimation of joint shear strength by the JRC（joint roughness coefficient）-JCS（joint compressive strength） model,natural rock joints of dif-ferent lithologic characteristics and different sizes were selected as samples,and their shear strengths under dry and saturated conditions were measured by direct shear test and compared to those esti-mated by the JRC-JCS model.Comparison results show that for natural rock joints with joint surfaces closely matched,the average relative error of joint shear strength between empirical estimation and direct shear test is 9.9%;the reliability of the empirical estimation of joint shear strength by the JRC-JCS model is good under both dry and saturated conditions if the JRC is determined accounting for directional statistical measurements,scale effect and surface smoothing during shearing.However,for natural rock joints with joint surfaces mismatched,the average relative error of joint shear strength between empirical estimation and direct shear test is 39.9%;the reliability of empirical estimation of joint shear strength by the JRC-JCS model is questionable under both dry and saturated conditions.

Empirical Bayes Estimation for the Parameter of Two-dimen sional One-side Truncated Distribution Families with Linex Loss

In this paper, we construct the EB estim ation for the parameter of the two-dimensional one side truncat ed distribution fam ilies using Linex loss. The convergence rate of EB estimation is given and it is shown that the proposed empirical Bayes estimaiton can be arbitrarily close to 1 under certain conditions.

Empirical Bayes Absolute Error Loss Estimation for Parameter of One-Side Truncation Distribution Families

In this paper we propose an absolute error loss EB estimator for parameter of one-side truncation distribution families. Under some conditions we have proved that the convergence rates of its Bayes risk is o, where 0<λ,r≤1,Mn≤lnln n (for large n),Mn→∞ as n→∞.

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 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.

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.

Asymptotically Optimal and Admissible Empirical Bayes Estimation of Normal Parameter

Under square loss, this paper constructs the empirical Bayes（EB） estimation for the parameter of normal distribution which has both asymptotic optimality and admissibility. Moreover, the convergence rate of the EB estimation obtained is proved to be O（n^-1）.

Empirical Estimates of Global Climate Sensitivity:An Assessment of Strategies Using a Coupled GCM

A control integration with the normal solar constant and one with it increased by 2.5% in the National Center for Atmospheric Research （NCAR） coupled atmosphere-ocean Climate System Model were conducted to see how well the actual realized global warming could be predicted just by analysis of the control results. This is a test, within a model context, of proposals that have been advanced to use knowledge of the present day climate to make ＂empirical＂ estimates of global climate sensitivity. The scaling of the top-of-the-atmosphere infrared flux and the planetary albedo as functions of surface temperature was inferred by examining four different temporal and geographical variations of the control simulations. Each of these inferences greatly overestimates the climate sensitivity of the model, largely because of the behavior of the cloud albedo. In each inference the control results suggest that cloudiness and albedo decrease with increasing surface temperature. However, the experiment with the increased solar constant actually has higher albedo and more cloudiness at most latitudes. The increased albedo is a strong negative feedback, and this helps account for the rather weak sensitivity of the climate in the NCAR model. To the extent that these model results apply to the real world, they suggest empirical evaluation of the scaling of global-mean radiative properties with surface temperature in the present day climate provides little useful guidance for estimates of the actual climate sensitivity to global changes.

Superiority of empirical Bayes estimation of error variance in linear model

In this paper, the Bayes estimator of the error variance is derived in a linear regression model, and the parametric empirical Bayes estimator （PEBE） is constructed. The superiority of the PEBE over the least squares estimator （LSE） is investigated under the mean square error （MSE） criterion. Finally, some simulation results for the PEBE are obtained.

Empirical Likelihood for Generalized Linear Models with Longitudinal Data

Generalized linear models are usually adopted to model the discrete or nonnegative responses.In this paper,empirical likelihood inference for fixed design generalized linear models with longitudinal data is investigated.Under some mild conditions,the consistency and asymptotic normality of the maximum empirical likelihood estimator are established,and the asymptotic χ^(2) distribution of the empirical log-likelihood ratio is also obtained.Compared with the existing results,the new conditions are more weak and easy to verify.Some simulations are presented to illustrate these asymptotic properties.

EMPIRICAL LIKELIHOOD INFERENCE FOR LOGISTIC EQUATION WITH RANDOM PERTURBATION

Empirical likelihood(EL) combined with estimating equations(EE) provides a modern semi-parametric alternative to classical estimation techniques such as maximum likelihood estimation(MLE). This paper not only uses closed form of conditional expectation and conditional variance of Logistic equation with random perturbation to perform maximum empirical likelihood estimation(MELE) for the model parameters, but also proposes an empirical likelihood ratio statistic(ELRS) for hypotheses concerning the interesting parameter. Monte Carlo simulation results show that MELE and ELRS provide competitive performance to parametric alternatives.

On nonparametric change point estimator based on empirical characteristic functions

We propose a nonparametric change point estimator in the distributions of a sequence of independent observations in terms of the test statistics given by Huˇskov′a and Meintanis(2006) that are based on weighted empirical characteristic functions. The weight function ω(t; a) under consideration includes the two weight functions from Huˇskov′a and Meintanis(2006) plus the weight function used by Matteson and James(2014),where a is a tuning parameter. Under the local alternative hypothesis, we establish the consistency, convergence rate, and asymptotic distribution of this change point estimator which is the maxima of a two-side Brownian motion with a drift. Since the performance of the change point estimator depends on a in use, we thus propose an algorithm for choosing an appropriate value of a, denoted by a_s which is also justified. Our simulation study shows that the change point estimate obtained by using a_s has a satisfactory performance. We also apply our method to a real dataset.

Weighted quantile regression for longitudinal data using empirical likelihood

This paper proposes a new weighted quantile regression model for longitudinal data with weights chosen by empirical likelihood(EL). This approach efficiently incorporates the information from the conditional quantile restrictions to account for within-subject correlations. The resulted estimate is computationally simple and has good performance under modest or high within-subject correlation. The efficiency gain is quantified theoretically and illustrated via simulation and a real data application.

Empirical Likelihood-based Inferences in Varying Coefficient Models with Missing Data

In this paper, we consider the empirical likelihood-based inferences for varying coefficient models Y = X^τα（U） ＋ ε when X are subject to missing at random. Based on the inverse probability-weighted idea, a class of empirical log-likelihood ratios, as well as two maximum empirical likelihood estimators, are developed for α（u）. The resulting statistics are shown to have standard chi-squared or normal distributions asymptotically.Simulation studies are also constructed to illustrate the finite sample properties of the proposed statistics.

EMPIRICAL LIKELIHOOD APPROACH FOR LONGITUDINAL DATA WITH MISSING VALUES AND TIME-DEPENDENT COVARIATES

Missing data and time-dependent covariates often arise simultaneously in longitudinal studies,and directly applying classical approaches may result in a loss of efficiency and biased estimates.To deal with this problem,we propose weighted corrected estimating equations under the missing at random mechanism,followed by developing a shrinkage empirical likelihood estimation approach for the parameters of interest when time-dependent covariates are present.Such procedure improves efficiency over generalized estimation equations approach with working independent assumption,via combining the independent estimating equations and the extracted additional information from the estimating equations that are excluded by the independence assumption.The contribution from the remaining estimating equations is weighted according to the likelihood of each equation being a consistent estimating equation and the information it carries.We show that the estimators are asymptotically normally distributed and the empirical likelihood ratio statistic and its profile counterpart follow central chi-square distributions asymptotically when evaluated at the true parameter.The practical performance of our approach is demonstrated through numerical simulations and data analysis.

Measurement of Joint Roughness Coefficient by Using Profilograph and Roughness Ruler

Joint roughness coefficient（JRC） is the key parameter for the empirical estimation of joint shear strength by using the JRC-JCS（joint wall compressive strength） model.Because JRC has such characteristics as nonuniformity,anisotropy,and unhomogeneity,directional statistical measurement of JRC is the precondition for ensuring the reliability of the empirical estimation method.However,the directional statistical measurement of JRC is time-consuming.In order to present an ideal measurement method of JRC,new profilographs and roughness rulers were developed according to the properties of rock joint undulating shape based on the review of measurement methods of JRC.Operation methods of the profilographs and roughness rulers were also introduced.A case study shows that the instruments and operation methods produce an effective means for the statistical measurement of JRC.

Estimating Complex Covariance by Observing Two Variables at a Time

The estimation of covariance matrices is central in array signal processing systems. This note addresses complex covariance estimation for the situation, where the complex data are available only as independent pairwise sets （observations） corresponding to individual elements of the matrix. The formulation for the empirical estimate and the normal maximum likelihood estimate is developed for the general case of different sample sizes for each observation. The approach allows, for example, the estimate of the p by p covariance matrix of a p-port sensor array from a two-port measurement instrument.