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51.
Doksum Kjell 《中国科学A辑(英文版)》2004,47(1):114-127
Let f(x) be the density of a design variable X and m(x) = E[Y\X = x] the regression function. Then m(x) - G(x)/f(x), where G(x) = m(x)f(x). The Dirac δ-function is used to define a generalized empirical function Gn (x) for G(x) whose expectation equals G(x). This generalized empirical function exists only in the space of Schwartz distributions, so we introduce a local polynomial of order p approximation to Gn(.) which provides estimators of the function G(x) and its derivatives. The density f(x) can be estimated in a similar manner. The resulting local generalized empirical estimator (LGE) of m(x) is exactly the Nadaraya-Watson estimator at interior points when p = 1, but on the boundary the estimator automatically corrects the boundary effect. Asymptotic normality of the estimator is established. Asymptotic expressions for the mean squared errors are obtained and used in bandwidth selection. Boundary behavior of the estimators is investigated in details. We use Monte Carlo simulations to show that the 相似文献
52.
Fuqing Gao 《Journal of Theoretical Probability》2003,16(2):401-418
Let f
n
be the non-parametric kernel density estimator based on a kernel function K and a sequence of independent and identically distributed random variables taking values in
d
. It is proved that if the kernel function is an integrable function with bounded variation, and the common density function f of the random variables is continuous and f(x) 0 as |x| , then the moderate deviation principle and large deviation principle for
hold. 相似文献
53.
P. Kabaila 《Acta Appl Math》2003,78(1-3):185-192
We consider the problem of constructing a 1– upper confidence limit for the scalar parameter 0 in the presence of the nuisance parameter vector 0, when the data are discrete. The 'profile plug-in' upper confidence limit is introduced by Kabaila and Lloyd. This confidence limit is based on computing a P-value
from an estimator
of 0, replacing the nuisance parameter by the profile maximum likelihood estimate
for known, and equating to . Theoretical and numerical evidence for the good coverage properties of this confidence limit is presented by Kabaila and Lloyd. An upper confidence limit should be assessed not only by its coverage properties but also by how large this confidence limit is. We measure how large the profile plug-in upper limit is by using a large sample approximation to it. This large sample approximation is used to delineate further the good properties of this confidence limit. 相似文献
54.
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
55.
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
56.
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
57.
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
58.
59.
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
60.
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