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51.
Consider a regular diffusion process X with finite speed measure m. Denote the normalized speed measure by μ. We prove that the uniform law of large numbers
holds if the class
has an envelope function that is μ-integrable, or if
is bounded in L
p(μ) for some p>1. In contrast with uniform laws of large numbers for i.i.d. random variables, we do not need conditions on the ‘size’ of
the class
in terms of bracketing or covering numbers. The result is a consequence of a number of asymptotic properties of diffusion
local time that we derive. We apply our abstract results to improve consistency results for the local time estimator (LTE)
and to prove consistency for a class of simple M-estimators.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
52.
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. 相似文献
53.
Xian Zhou Xiaoqian Sun Jinglong Wang 《Annals of the Institute of Statistical Mathematics》2001,53(4):760-768
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. 相似文献
54.
If (Xi, 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 fn, a kernel estimator of f, and f0, or between fn 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). 相似文献
55.
56.
小波变换轮廓术的测量范围研究 总被引:2,自引:1,他引:2
利用小波“脊”处的小波系数来提取变形条纹中的相位信息可以在很大程度上抑制条纹图中有用的基频分量与零频和其它谐波频率分量的混叠,弥补了傅里叶变换轮廓术的不足。从离散信号频域分析角度,推导了变形条纹小波变换的频谱描述形式,讨论了其测量范围,包括结构条件和抽样条件。结果表明,只有在无周期内瞬时频谱混叠,即任意位置处物体瞬时高度变化满足h/xx=b<1/3条件时,和不存在抽样引起的周期间瞬时频谱混叠的抽样条件下(即一个周期内的抽样点数m≥4时),小波变换轮廓术才能正确恢复被测物体的三维面型。计算机模拟和实验验证了该结论。 相似文献
57.
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. 相似文献
58.
Manoj Chacko P. Yageen Thomas 《Annals of the Institute of Statistical Mathematics》2008,60(2):301-318
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. 相似文献
59.
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. 相似文献
60.
A LAW OF ITERATED LOGARITHM FOR THE MLE IN A RANDOM CENSORING MODEL WITH INCOMPLETE INFORMATION 总被引:1,自引:0,他引:1
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. 相似文献