共查询到20条相似文献,搜索用时 15 毫秒
1.
Shie-Shien Yang 《Annals of the Institute of Statistical Mathematics》1981,33(1):463-470
Summary Let (X
1,Y
1), (X
2,Y
2),…, (X
n,Y
n) be i.i.d. as (X, Y). TheY-variate paired with therth orderedX-variateX
rn is denoted byY
rn and terms the concomitant of therth order statistic. Statistics of the form
are considered. The asymptotic normality ofT
n is established. The asymptotic results are used to test univariate and bivariate normality, to test independence and linearity
ofX andY, and to estimate regression coefficient based on complete and censored samples. 相似文献
2.
3.
4.
Jugal Ghorai 《Annals of the Institute of Statistical Mathematics》1980,32(1):341-350
LetX
1,...,X
n
be i.i.d. random variable with a common densityf. Let
be an estimate off(x) based on a complete orthonormal basis {φ
k
:k≧0} ofL
2[a, b]. A Martingale central limit theorem is used to show that
, where
and
. 相似文献
5.
Ibrahim A. Ahmad 《Annals of the Institute of Statistical Mathematics》1982,34(1):39-53
Summary By representing the location and scale parameters of an absolutely continuous distribution as functionals of the usually unknown
probability density function, it is possible to provide estimates of these parameters in terms of estimates of the unknown
functionals.
Using the properties of well-known methods of density estimates, it is shown that the proposed estimates possess nice large
sample properties and it is indicated that they are also robust against dependence in the sample. The estimates perform well
against other estimates of location and scale parameters. 相似文献
6.
In the model of sequential order statistics, prior distributions are considered for the model parameters, which, for example, describe increasing load put on remaining components. Gamma priors are examined as well as priors out of a class of extended truncated Erlang distributions (ETED), which is introduced along with some properties. The choice of independent priors in both set-ups leads to respective independent, conjugate posterior distributions for the model parameters of sequential order statistics. Since, in practical applications, the model parameters will often be increasingly ordered, a multivariate prior is applied being the joint distribution of common ETED-order statistics. Whatever baseline distribution of the sequential order statistics is chosen, the joint posterior distribution turns out to be a Weinman multivariate exponential distribution. Posterior moments are given explicitly, and HPD credible sets for the model parameters are stated. 相似文献
7.
Ibrahim A. Ahmad 《Annals of the Institute of Statistical Mathematics》1979,31(1):279-288
Among several widely use methods of nonparametric density estimation is the technique of orthogonal series advocated by several
authors. For such estimate when the observations are assumed to have been taken from strong mixing sequence in the sense of
Rosenblatt [7] we study strong consistency by developing probability inequality for bounded strongly mixing random variables.
The results obtained are then applied to two estimates of the functional Δ(f)=∫f
2
(x)dx were strong consistency is established. One of the suggested two estimates of Δ(f) was recently studied by Schuler and Wolff [8] in the case of independent and identically distributed observations where
they established consistency in the second mean of the estimate.
Research supported in part by the National Research Council of Canada and in part by McMaster University Research Board. Now
at Memphis State University, Memphis, Tennessee 38152, U.S.A. 相似文献
8.
K. F. Cheng 《Annals of the Institute of Statistical Mathematics》1982,34(1):479-489
Summary Letf
n
(p)
be a recursive kernel estimate off
(p) thepth order derivative of the probability density functionf, based on a random sample of sizen. In this paper, we provide bounds for the moments of
and show that the rate of almost sure convergence of
to zero isO(n
−α), α<(r−p)/(2r+1), iff
(r),r>p≧0, is a continuousL
2(−∞, ∞) function. Similar rate-factor is also obtained for the almost sure convergence of
to zero under different conditions onf.
This work was supported in part by the Research Foundation of SUNY. 相似文献
9.
The paper presents a unified approach to local likelihood estimation for a broad class of nonparametric models, including
e.g. the regression, density, Poisson and binary response model. The method extends the adaptive weights smoothing (AWS) procedure
introduced in Polzehl and Spokoiny (2000) in context of image denoising. The main idea of the method is to describe a greatest
possible local neighborhood of every design point Xi in which the local parametric assumption is justified by the data. The method is especially powerful for model functions
having large homogeneous regions and sharp discontinuities. The performance of the proposed procedure is illustrated by numerical
examples for density estimation and classification. We also establish some remarkable theoretical nonasymptotic results on
properties of the new algorithm. This includes the ``propagation' property which particularly yields the root-n consistency
of the resulting estimate in the homogeneous case. We also state an ``oracle' result which implies rate optimality of the
estimate under usual smoothness conditions and a ``separation' result which explains the sensitivity of the method to structural
changes. 相似文献
10.
Peter Hall 《Annals of the Institute of Statistical Mathematics》1980,32(1):351-362
The kernel method of density estimation is not so attractive when the density has its support confined to (0, ∞), particularly
when the density is unsmooth at the origin. In this situation the method of orthogonal series is competitive. We consider
three essentially different orthogonal series—those based on the even and odd Hermite functions, respectively, and that based
on Laguerre functions—and compare them from the point of view of mean integrated square error. 相似文献
11.
M. Burkschat 《Journal of multivariate analysis》2009,100(6):1093-1106
Multivariate dependence of spacings of generalized order statistics is studied. It is shown that spacings of generalized order statistics from DFR (IFR) distributions have the CIS (CDS) property. By restricting the choice of the model parameters and strengthening the assumptions on the underlying distribution, stronger dependence relations are established. For instance, if the model parameters are decreasingly ordered and the underlying distribution has a log-convex decreasing (log-concave) hazard rate, then the spacings satisfy the MTP2 (S- MRR2) property. Some consequences of the results are given. In particular, conditions for non-negativity of the best linear unbiased estimator of the scale parameter in a location-scale family are obtained. By applying a result for dual generalized order statistics, we show that in the particular situation of usual order statistics the assumptions can be weakened. 相似文献
12.
Ibrahim A. Ahmad 《Annals of the Institute of Statistical Mathematics》1982,34(1):457-466
L
p notion of the weak, mean, and strong consistency of the kernel method of multivariate density estimation is proposed and
studied. The results expand, unify, or generalize most known results in the literature. Rates of convergence in mean and strongL
p-consistencies are presented. 相似文献
13.
B. Gyires 《Periodica Mathematica Hungarica》1978,9(1-2):109-113
This paper contains applications of theorems of [1] for quadratic statistics which have constant regression on linear statistics. Two theorems are proved. The first is a sufficient condition which assumes that the characteristic function of a sample is an entire function. The second gives a new characterization of the normal distribution. 相似文献
14.
W. Gawronski 《Periodica Mathematica Hungarica》1985,16(1):23-43
Starting from the classical theorem of Weierstrass (and its modifications) on approximation of continuous functions by means of Bernstein polynomials a smoothed histogram type estimator is developed for estimating probability densities and its derivatives. Consistency results are obtained in form of various strong laws. In particular, one gets estimates for the rates for pointwise and uniform strong convergence of estimators for the derivatives. Moreover, for approximating the density itself the exact order of consistency is established. This is done by a law of iterated logarithm for pointwise approximation and by a law of logarithm in case of uniform approximation.This paper contains parts of the author's Habilitationsschrift written at the Department of Mathematics of the University of Ulm. 相似文献
15.
Richard A. Vitale 《Acta Appl Math》1987,9(1-2):97-102
Using the expectation of a particular random set, we present a multivariate extension of a characterization theorem involving extreme order statistics.Supported in part by National Science Foundation grant DMS 8603944. 相似文献
16.
U. Stadtmüller 《Periodica Mathematica Hungarica》1986,17(2):83-108
We consider a class of nonparametric estimators for the regression functionm(t) in the model:y
i
=m(t
i
) +
i
, 1 i n, t
i
[0, 1], which are linear in the observationsy
i
. Several limit theorems concerning local and global stochastic and a.s. convergence and limit distributions are given. 相似文献
17.
Some fundamental properties of the empirical distribution functions are derived in the case of mixing random variables. These properties are then utilized to study asymptotic normality and strong laws of large numbers for functions of order statistics. 相似文献
18.
A. L. Wright 《Annals of the Institute of Statistical Mathematics》1980,32(1):95-97
It is shown that there does not exist a complete sufficient statistic for the class of allk-state Markov chains,k≧3. Whenk=2 there is a complete sufficient statistic. 相似文献
19.
Let be the classical kernel density estimator based on a kernel K and n independent random vectors X
i
each distributed according to an absolutely continuous law on . It is shown that the processes , , converge in law in the Banach space , for many interesting classes of functions or sets, some -Donsker, some just -pregaussian. The conditions allow for the classical bandwidths h
n
that simultaneously ensure optimal rates of convergence of the kernel density estimator in mean integrated squared error,
thus showing that, subject to some natural conditions, kernel density estimators are ‘plug-in’ estimators in the sense of
Bickel and Ritov (Ann Statist 31:1033–1053, 2003). Some new results on the uniform central limit theorem for smoothed empirical
processes, needed in the proofs, are also included.
相似文献
20.
Ibrahim A. Ahmad 《Annals of the Institute of Statistical Mathematics》1981,33(1):247-254
Summary A general method based on “delta sequences” due to Walter and Blum [12] is extended to sequences of strictly stationary mixing
random variables having the same marginal distribution admitting a Lebesgue probability density function. It is proved that,
under certain conditions, the rate of mean square convergence obtained in the i.i.d. case by Walter and Blum, continues to
hold.
University of Petroleum and Minerals 相似文献