η%-Superconvergence of Finite Element Solutions and Error Estimators

This paper is a summary of our study on the superconvergence of the finite element solutions and error estimators. We will persent the analysis of %-superconvergence for finite element solutions of the Poisson equation in the interior of meshes of triangles with straight edges, as well as the analysis at the boundary. The %-superconvergence via local averaging will also be presented, and the error estimators are compared in the sense of %-superconvergence.     

Estimation of the Multivariate Normal Precision Matrix under the Entropy Loss

Let X ₁, , X _n (n > p) be a random sample from multivariate normal distribution N _p (, ), where R ^p and is a positive definite matrix, both and being unknown. We consider the problem of estimating the precision matrix ^–1. In this paper it is shown that for the entropy loss, the best lower-triangular affine equivariant minimax estimator of ^–1 is inadmissible and an improved estimator is explicitly constructed. Note that our improved estimator is obtained from the class of lower-triangular scale equivariant estimators.     

Local Power Properties of Kernel Based Goodness of Fit Tests

If (X_i, i ) is a strictly stationary process with marginal density function f, we are interested in testing the hypothesis H₀: {f=f₀}, where f₀ is given. We consider different test statistics based on integrated quadratic forms measuring the proximity between f_n, a kernel estimator of f, and f₀, or between f_n and its expected value computed under H₀. We study the asymptotic local power properties of the testing procedures under local alternatives. This study generalizes to the multidimensional case in a context of dependence the corresponding one made by P. J. Bickel and M. Rosenblatt in 1973 (Ann. Statist.1, 1071–1095).     

基于多元局部多项式方法的混沌时间序列预测

根据Takens定理，把混沌时间序列构造为一组序列对，然后用多元局部多项式方法来预测其序列.这种核估计方法可以结合局域法与全局法的优点，使得预测的精度更高.仿真结果表明，该方法非常有效.     

Stability of principal components

In this article we deal with the problem of stability of the conclusions from principal components analysis over repeated samples. We define a measure of stability for each component and investigate some of the measures properties. We then obtain the maximum likelihood estimators (MLEs) of the measures, and derive their joint limiting distributions. The MLEs of the measures turn out to be asymptotically unbiased and jointly have the multivariate normal distribution. Modified estimators are also found to reduce the amount of bias in the MLEs. To facilitate interpretation of the measures we define stability confidence level as coverage probability, and associate with each measure a stability confidence level to describe the measure in terms of probability. Finally, we investigate the stability of the components via a simulation study and compare the performance of the MLEs and the modified estimators in terms of bias and precision. This work was sponsored by a grant from the Office of Vice-President for Research at Kuwait University under project number SS049.     

Estimation of a parameter of Morgenstern type bivariate exponential distribution by ranked set sampling

Ranked set sampling is applicable whenever ranking of a set of sampling units can be done easily by a judgement method or based on the measurement of an auxiliary variable on the units selected. In this work, we consider ranked set sampling, in which ranking of units are done based on measurements made on an easily and exactly measurable auxiliary variable X which is correlated with the study variable Y. We then estimate the mean of the study variate Y by the BLUE based on the measurements made on the units of the ranked set sampling regarding the study variable Y, when (X ,Y) follows a Morgenstern type bivariate exponential distribution. We then consider unbalanced multistage ranked set sampling and estimate the mean of the study variate Y by the BLUE based on the observations made on the units of multistage ranked set sample regarding the study variable Y. Efficiency comparison is also made on all estimators considered in this work.     

Bootstrap tests for unit roots in seasonal autoregressive models

This paper proposes bootstrap tests for the presence of unit roots in a seasonal autoregressive model. The asymptotic validity of the proposed bootstrap scheme is established, and Monte Carlo experiments are used to investigate the small-sample performance of the tests.     

A LAW OF ITERATED LOGARITHM FOR THE MLE IN A RANDOM CENSORING MODEL WITH INCOMPLETE INFORMATION

In this article, a law of iterated logarithm for the maximum likelihood estimator in a random censoring model with incomplete information under certain regular conditions is obtained.     

A Moderate Deviation Principle for <Emphasis Type="Italic">m</Emphasis>-Dependent Random Variables with Unbounded <Emphasis Type="Italic">m</Emphasis>

In this paper, a theorem on the moderate deviation principle for random arrays under m-dependence with unbounded m is established. This partially extends the results of Chen (Stat. Probab. Lett. 35:123–134, 1997). As an application, the moderate deviation principle for the truncation estimator of the variance in the analysis of time series is obtained.      

约束最小二乘估计的优良性

对于线性模型y=Xθ ε,ε服从椭球等高单峰分布,未知参数θ满足不等式约束a′θ≥0,证明了在参数估计优良性的集中概率准则下,θ的约束最小二乘估计θ~*优于最小二乘估计θ.