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Maximum likelihood, unbiased estimation, Rao-Blackwell and Lehmann-Scheffe theorems, information inequality, asymptotic relative efficiency of estimators.

点估计和区间估计的一般方法,估计量的小样本和大样本性质:矩法,极大似然估计,无偏估计,Rao-Blackwell 和Lehmann-Scheffe 理论,信息不等式,渐进相对有效估计量。

There are two findings summarized from previous studies:(1) the least squares estimator is a common choice of researchers, but under an unequal probability design, the estimator is biased,(2) the probability weighted estimator is consistent but may have a large variance.

过去的研究发现:(1)在不等机率抽样时,一般常用的最小平方法所得到的回归参数估计式并非不偏估计式;(2)机率加权最小平方法可以改善不偏性,然却增加估计的变异程度。

In this paper we discuss the influence problem of Ridge Estimator in general linear regression model, study the influence analysis on Ridge Estimator with covariance matrix disturbance and data deletion, define Cook distance of Rideg Estimator based on biased estimator.

讨论一般线性回归模型岭估计的影响+分析问题,研究了协方差阵扰动和数据删除对岭估计的影响,给出了岭估计基于有偏估计的Cook距离。

To the problem of unbiasedness of L 1 estimation,basing on uniqueness of solution,Zhou Shijiang proved it according to dual theorem of linear programming; and Wang Zhizhong proved it according to probability statistics theorem by using the method from special to general; also,basing on error distribution theorem and probability statistics theorem,the authors proved it.

对于L1 估计的无偏性问题,周世健基于解法的惟一性,根据线性规划的对偶理论,证明了L1 估计的无偏性[5] ;王志忠根据数理统计理论,采用由特殊情形推广到一般情形的方法,证明了L1 估计的无偏性[6] 。

Dorea advanced kernel estimation p of p ,which is a general density with respect to a σ-finite measure v on.ξ is a σ-field of subsets of ER. Some qualities have been gotten. And it has been proved that those results consist of theories of classical kernel estimation for continual density and further extended theories of disperse kernel estimation.

Y Dorea在2001年提出了关于上的σ-有限测度v的一般密度函数P的核估计几,其中ER,ξ是E的一个σ-域,得到了一些结果,并且验证了所得结论包含经典的连续密度核估计的结论,还进一步延伸了离散分布核估计的结论。

Finally, in the third section, by constructing some functional which similar to the conservation law of evolution equation and the technical estimates, we prove that in the inviscid limit the solution of generalized derivative Ginzburg—Landau equation converges to the solution of derivative nonlinear Schrodinger equation correspondently in one-dimension; The existence of global smooth solution for a class of generalized derivative Ginzburg—Landau equation are proved in two-dimension, in some special case, we prove that the solution of GGL equation converges to the weak solution of derivative nonlinear Schr〓dinger equation; In general case, by using some integral identities of solution for generalized Ginzburg—Landau equations with inhomogeneous boundary condition and the estimates for the L〓 norm on boundary of normal derivative and H〓 norm of solution, we prove the existence of global weak solution of the inhomogeneous boundary value problem for generalized Ginzburg—Landau equations.

第三部分:在一维情形,我们考虑了一类带导数项的Ginzburg—Landau方程,通过构造一些类似于发展方程守恒律的泛函及巧妙的积分估计,证明了当粘性系数趋于零时,Ginzburg—Landau方程的解逼近相应的带导数项的Schr〓dinger方程的解,并给出了最优收敛速度估计;在二维情形,我们证明了一类带导数项的广义Ginzburg—Landau方程整体光滑解的存在性,以及在某种特殊情形下,GL方程的解趋近于相应的带导数项的Schr〓dinger方程的弱解;在一般情形下,我们讨论了一类Ginzburg—Landau方程的非齐次边值问题,通过几个积分恒等式,同时估计解的H〓模及法向导数在边界上的模,证明了整体弱解的存在性。

Then, we discuss a robust implementation of the pilot-symbol-aided estimator that is insensive to channel statistics. The analysis of these algorithms is made by computer simulation. Finally, combinating with the application of channel estimation , we present two techniques: STBC (space-time block coding) and STTC (space-time trellis coding) to improve the performance of channel parameter estimation.

在基于导频的估计中,研究了基于MMSE下二维导频辅助信道估计,并结合无线信道的统计特性在一般不可知的条件下,给出了一种对无线信道的统计特性不是很敏感的鲁棒的二维导频辅助信道估计器,通过实验仿真证明其有效性。

The nonlinearity and discrete gradient inherited in CAViaR model is a conundrum for parameter estimation. We take the asymmetric Laplace distribution with scale parameter as the error process; indicate the variance has a minimum positive value when the scale parameter is a constant, conflicting with the distribution of real financial data. Further we estimate the parameters of indirect TARCH-CAViaR model base on Bayesian framework and Markov chain Monte Carlo method. The optimal scale parameter can also be obtained by Markov chain Monte Carlo method.

CAViaR一般模型中递归分位回归方程的非线性和非连续可微性是参数估计的一个难题,基于含有尺度参数的不对称拉普拉斯分布作为误差过程,指出将尺度参数固定为常数会导致不对称拉普拉斯分布随机变量的方差存在最小正值的限制,与实际金融数据分布不符;进而提出采用贝叶斯分析和马尔科夫链蒙特卡罗模拟方法,估计间接TARCH-CAViaR模型的参数,并可获得尺度参数的合理估计。

Ects, the covariance matrix of observation vector has special structure,and using the linear transformation for original model by idempotent matricesin the spectral decomposition of the covariance matrix, the problem of estima-tion of the covariance matrix becomes simultaneous estimation of all the distincteigenvalues of it.

在带有随机回归系数的一般线性模型中,首次提出了随机回归系数和参数的Minimax估计问题,分别在齐次线性估计类和一切估计类中研究了一个线性估计的Minimax性。

In addition, because motion vectors must be estimated in the process of region's motion parameters estimation, this paper discussed the theory and general methods of two-dimensional motion estimation and proposes a fast motion estimation algorithm based on the prediction of neighbour block's motion vector.

此外,由于在区域的运动参数估计过程中涉及到对运动矢量的估计,因此本文还讨论了二维运动矢量估计的原理和一般方法,并提出了一种基于邻域子块的运动矢量预测的快速运动估计算法。

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