Comparison and combination of EAKF and SIR-PF in the Bayesian filter framework

Bayesian estimation theory provides a general approach for the state estimate of linear or nonlinear and Gaussian or non-Gaussian systems. In this study, we first explore two Bayesian-based methods： ensemble adjustment Kalman filter（EAKF） and sequential importance resampling particle filter（SIR-PF）, using a well-known nonlinear and non-Gaussian model（Lorenz ＇63 model）. The EAKF, which is a deterministic scheme of the ensemble Kalman filter（En KF）, performs better than the classical（stochastic） En KF in a general framework. Comparison between the SIR-PF and the EAKF reveals that the former outperforms the latter if ensemble size is so large that can avoid the filter degeneracy, and vice versa. The impact of the probability density functions and effective ensemble sizes on assimilation performances are also explored. On the basis of comparisons between the SIR-PF and the EAKF, a mixture filter, called ensemble adjustment Kalman particle filter（EAKPF）, is proposed to combine their both merits. Similar to the ensemble Kalman particle filter, which combines the stochastic En KF and SIR-PF analysis schemes with a tuning parameter, the new mixture filter essentially provides a continuous interpolation between the EAKF and SIR-PF. The same Lorenz ＇63 model is used as a testbed, showing that the EAKPF is able to overcome filter degeneracy while maintaining the non-Gaussian nature, and performs better than the EAKF given limited ensemble size.

Minimum MSE Weighted Estimator to Make Inferences for a Common Risk Ratio across Sparse Meta-Analysis Data

The paper aims to discuss three interesting issues of statistical inferences for a common risk ratio (RR) in sparse meta-analysis data. Firstly, the conventional log-risk ratio estimator encounters a number of problems when the number of events in the experimental or control group is zero in sparse data of a 2 × 2 table. The adjusted log-risk ratio estimator with the continuity correction points based upon the minimum Bayes risk with respect to the uniform prior density over (0, 1) and the Euclidean loss function is proposed. Secondly, the interest is to find the optimal weights of the pooled estimate that minimize the mean square error (MSE) of subject to the constraint on where , , . Finally, the performance of this minimum MSE weighted estimator adjusted with various values of points is investigated to compare with other popular estimators, such as the Mantel-Haenszel (MH) estimator and the weighted least squares (WLS) estimator (also equivalently known as the inverse-variance weighted estimator) in senses of point estimation and hypothesis testing via simulation studies. The results of estimation illustrate that regardless of the true values of RR, the MH estimator achieves the best performance with the smallest MSE when the study size is rather large and the sample sizes within each study are small. The MSE of WLS estimator and the proposed-weight estimator adjusted by , or , or are close together and they are the best when the sample sizes are moderate to large (and) while the study size is rather small.

EMPIRICAL LIKELIHOOD CONFIDENCE REGION FOR PARAMETERS IN LINEAR ERRORS-IN-VARIABLES MODELS WITH MISSING DATA

The multivariate linear errors-in-variables model when the regressors are missing at random in the sense of Rubin （1976） is considered in this paper. A constrained empirical likelihood confidence region for a parameter β0 in this model is proposed, which is constructed by combining the score function corresponding to the weighted squared orthogonal distance based on inverse probability with a constrained region of β0. It is shown that the empirical log-likelihood ratio at the true parameter converges to the standard chi-square distribution. Simulations show that the coverage rate of the proposed confidence region is closer to the nominal level and the length of confidence interval is narrower than those of the normal approximation of inverse probability weighted adjusted least square estimator in most cases. A real example is studied and the result supports the theory and simulation＇s conclusion.

Parameter Estimation of Varying Coefficients Structural EV Model with Time Series

In this paper, the parameters of a p-dimensional linear structural EV(error-in-variable)model are estimated when the coefficients vary with a real variable and the model error is time series.The adjust weighted least squares(AWLS) method is used to estimate the parameters. It is shown that the estimators are weakly consistent and asymptotically normal, and the optimal convergence rate is also obtained. Simulations study are undertaken to illustrate our AWLSEs have good performance.

On Two-stage Estimate Based on Independent Estimate of Covariance Matrix

When an independent estimate of covariance matrix is available, we often prefer two-stage estimate （TSE）. Expressions of exact covarianee matrix of the TSE obtained by using all and some covariables in eovariance adjustment approach are given, and a necessary and sufficient condition for the TSE to be superior to the least square estimate and related large sample test is also established. Furthermore the TSE, by using some covariables, is expressed as weighted least square estimate. Basing on this fact, a necessary and sufficient condition for the TSE by using some covariables to be superior to the TSE by using all eovariables is obtained. These results give us some insight into the selection of covariables in the TSE and its application.