共查询到20条相似文献,搜索用时 31 毫秒
1.
Jun Shao 《Annals of the Institute of Statistical Mathematics》1992,44(4):687-701
To estimate the dispersion of an M-estimator computed using Newton's iterative method, the jackknife method usually requires to repeat the iterative process n times, where n is the sample size. To simplify the computation, one-step jackknife estimators, which require no iteration, are proposed in this paper. Asymptotic properties of the one-step jackknife estimators are obtained under some regularity conditions in the i.i.d. case and in a linear or nonlinear model. All the one-step jackknife estimators are shown to be asymptotically equivalent and they are also asymptotically equivalent to the original jackknife estimator. Hence one may use a dispersion estimator whose computation is the simplest. Finite sample properties of several one-step jackknife estimators are examined in a simulation study.The research was supported by Natural Sciences and Engineering Research Council of Canada. 相似文献
2.
Delete-group Jackknife Estimate in
Partially Linear Regression Models with Heteroscedasticity 总被引:3,自引:0,他引:3
Abstract Consider a partially linear regression model with an unknown vector parameter β,an unknownfunction g(.),and unknown heteroscedastic error variances.Chen,You proposed a semiparametric generalizedleast squares estimator(SGLSE)for β,which takes the heteroscedasticity into account to increase efficiency.Forinference based on this SGLSE,it is necessary to construct a consistent estimator for its asymptotic covariancematrix.However,when there exists within-group correlation, the traditional delta method and the delete-1jackknife estimation fail to offer such a consistent estimator.In this paper, by deleting grouped partial residualsa delete-group jackknife method is examined.It is shown that the delete-group jackknife method indeed canprovide a consistent estimator for the asymptotic covariance matrix in the presence of within-group correlations.This result is an extension of that in[21]. 相似文献
3.
In statistics, it is usually difficult to estimate the probability density function from N independent samples X1,X2, …?, XN identically distributed. A lot of work has been done in the statistical literature on the problem of probability density estimation (e.g. Cencov, 1962; Devroye and Gyorfi, 1981; Hall, 1980 and 1982; Hominal, 1979; Izenman, 1991; Kronmal and Tarter, 1968; Parzen, 1962; Rosenblatt, 1956). In this paper, we consider random variables on bounded support. Orthogonal series estimators, studied in detail by Kronmal and Tarter (1968), by Hall (1982) and by Cencov (1962), show that there is a disadvantage related to the Gibbs phenomenon on the bias of these estimators. We suggest a new method for the non–parametric probability density function estimation based on the kernel method using an appropriately chosen regular change of variable. The new method can be used for several problems of signal processing applications (scalar or vector quantization, speech or image processing, pattern recognition, etc.). Applications to shape classification and speech coding are given. 相似文献
4.
Dale Umbach 《Journal of multivariate analysis》1978,8(4):518-531
The behavior of the posterior for a large observation is considered. Two basic situations are discussed; location vectors and natural parameters.Let X = (X1, X2, …, Xn) be an observation from a multivariate exponential distribution with that natural parameter Θ = (Θ1, Θ2, …, Θn). Let θx* be the posterior mode. Sufficient conditions are presented for the distribution of Θ − θx* given X = x to converge to a multivariate normal with mean vector 0 as |x| tends to infinity. These same conditions imply that E(Θ | X = x) − θx* converges to the zero vector as |x| tends to infinity.The posterior for an observation X = (X1, X2, …, Xn is considered for a location vector Θ = (Θ1, Θ2, …, Θn) as x gets large along a path, γ, in Rn. Sufficient conditions are given for the distribution of γ(t) − Θ given X = γ(t) to converge in law as t → ∞. Slightly stronger conditions ensure that γ(t) − E(Θ | X = γ(t)) converges to the mean of the limiting distribution.These basic results about the posterior mean are extended to cover other estimators. Loss functions which are convex functions of absolute error are considered. Let δ be a Bayes estimator for a loss function of this type. Generally, if the distribution of Θ − E(Θ | X = γ(t)) given X = γ(t) converges in law to a symmetric distribution as t → ∞, it is shown that δ(γ(t)) − E(Θ | X = γ(t)) → 0 as t → ∞. 相似文献
5.
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
6.
We consider the problem of estimating the discriminant coefficients, η=∑1-(θ(1)-θ(2)) based on two independent normal samples fromN
p
(θ(1),∑) andN
p
(θ(2),∑). We are concerned with the estimation of η as the gradient of log-odds between two extreme situations. A decision theoretic
approach is taken with the quadratic loss function. We derive the unbiased estimator of the essential part of the risk which
is applicable for general estimators. We propose two types of new estimators and prove their dominance over the traditional
estimator using this unbiased estimator. 相似文献
7.
Wulf Rehder 《Annals of the Institute of Statistical Mathematics》1980,32(1):179-185
Summary Linear unbiased estimation of the mean of a random variable in Hilbert space is treated in the typical case where the mean
belongs to a known subspace.
The best linear estimate depends on the underlying covariance operatorB
0 of the random variable. This operatorB
0, however, is rarely completely known, so that an auxiliary operatorB is used to compute a “pseudo-best” estimate. It is shown that the best and the pseudo-best estimates coincide, if and only
ifB
0
B
−1 leavesM invariant. Applications to linear regression are to be found in the references. 相似文献
8.
Summary Uniform (or type (B)
d
) asymptotic normality of the joint distribution of an increasing number of sample quantiles as the sample size increases
is investigated in both cases where the basic distributions are equal and are unequal. Under fairly general assumptions, sufficient
conditions are derived for the asymptotic normality of sample quantiles.
Type (B)
d
asymptotic normality is a strictly stronger notion than the usual one which is based on the convergence in law, and the results
obtained in this article will be helpful to widen the applicability of results on asymptotic normality of sample quantiles
to related statistical inferences. 相似文献
9.
Carla Henriques Paulo Eduardo Oliveira 《Statistical Inference for Stochastic Processes》2008,11(1):77-91
Let X
n
, n ≥ 1, be a strictly stationary associated sequence of random variables, with common continuous distribution function F. Using histogram type estimators we consider the estimation of the two-dimensional distribution function of (X
1,X
k+1) as well as the estimation of the covariance function of the limit empirical process induced by the sequence X
n
, n ≥ 1. Assuming a convenient decrease rate of the covariances Cov(X
1,X
n+1), n ≥ 1, we derive uniform strong convergence rates for these estimators. The condition on the covariance structure of the variables
is satisfied either if Cov(X
1,X
n+1) decreases polynomially or if it decreases geometrically, but as we could expect, under the latter condition we are able
to establish faster convergence rates. For the two-dimensional distribution function the rate of convergence derived under
a geometrical decrease of the covariances is close to the optimal rate for independent samples.
相似文献
10.
Isha Bagai B. L. S. Prakasa Rao 《Annals of the Institute of Statistical Mathematics》1995,47(2):253-266
Let {X
n
,n1} be a strictly stationary sequence of associated random variables defined on a probability space (,B, P) with probability density functionf(x) and failure rate functionr(x) forX
1. Letf
n
(x) be a kerneltype estimator off(x) based onX
1,...,X
n
. Properties off
n
(x) are studied. Pointwise strong consistency and strong uniform consistency are established under a certain set of conditions. An estimatorr
n
(x) ofr(x) based onf
n
(x) andF
n
(x), the empirical survival function, is proposed. The estimatorr
n
(x) is shown to be pointwise strongly consistent as well as uniformly strongly consistent over some sets. 相似文献
11.
We develop a method for taking target mass effects into account for the structure functions of inelastic lepton-hadron scattering
using analytic moments in the variable s instead of the well-known Nachtmann variable ξ and Bjorken variable x. We find new
expressions for the structure functions F
1, F
2, and F
3
that depend on the target mass and agree with the spectral property. 相似文献
12.
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
13.
In this paper, we focus our attention on the precise asymptotics of error variance estimator in partially linear regression
models, y
i
= x
i
τ
β + g(t
i
) + ε
i
, 1 ≤ i ≤ n, {ε
i
, i = 1, ⋯ n} are i.i.d random errors with mean 0 and positive finite variance σ
2. Following the ideas of Allan Gut and Aurel Spătaru[7,8] and Zhang[21], on precise asymptotics in the Baum-Katz and Davis laws of large numbers and precise rate in laws of the iterated logarithm,
respectively, and subject to some regular conditions, we obtain the corresponding results in partially linear regression models.
相似文献
14.
Let {X(t): t [a, b]} be a Gaussian process with mean μ L2[a, b] and continuous covariance K(s, t). When estimating μ under the loss ∫ab (
(t)−μ(t))2 dt the natural estimator X is admissible if K is unknown. If K is known, X is minimax with risk ∫ab K(t, t) dt and admissible if and only if the three by three matrix whose entries are K(ti, tj) has a determinant which vanishes identically in ti [a, b], i = 1, 2, 3. 相似文献
15.
Yasushi Nagata 《Annals of the Institute of Statistical Mathematics》1983,35(1):365-373
Summary Let a random variableX follow ap-variate normal distributionN
p
(θ, I
p
) with an unknownp×1 vector θ andp×p identity matrixI
p
. The admissibility of a preliminary test estimator using AIC (Akaike's Information Criterion) procedure will be shown ifp=1 and its inadmissibility will be shown ifp≧3 under the loss function based on Kullback-Leibler information measure. Furthermore the two sample case is also considered. 相似文献
16.
We present and study a procedure for testing the null hypothesis of multivariate elliptical symmetry. The procedure is based on the averages of some spherical harmonics over the projections of the scaled residual (1978, N. J. H. Small, Biometrika65, 657–658) of the d-dimensional data on the unit sphere of
d. We find, under mild hypothesis, the limiting null distribution of the statistic presented, showing that, for an appropriate choice of the spherical harmonics included in the statistic, this distribution does not depend on the parameters that characterize the underlying elliptically symmetric law. We describe a bivariate simulation study that shows that the finite sample quantiles of our statistic converge fairly rapidly, with sample size, to the theoretical limiting quantiles and that our procedure enjoys good power against several alternatives. 相似文献
17.
Xiaojing Xiang 《Journal of multivariate analysis》1996,59(2):206-216
Let (X1, Y1), (X2, Y2), …, be two-dimensional random vectors which are independent and distributed as (X, Y). For 0<p<1, letξ(px) be the conditionalpth quantile ofYgivenX=x; that is,ξ(px)=inf{y : P(YyX=x)p}. We consider the problem of estimatingξ(px) from the data (X1, Y1), (X2, Y2), …, (Xn, Yn). In this paper, a new kernel estimator ofξ(px) is proposed. The asymptotic normality and a law of the iterated logarithm are obtained. 相似文献
18.
Smiley W. Cheng 《Annals of the Institute of Statistical Mathematics》1983,35(1):407-414
Summary The most powerful test of the null hypothesisH
0:σ=σ
0 versus the alternative hypothesisH
1:σ=σ
1 based on a few selected sample quantiles is proposed here where σ is the scale parameter of the distribution and the location
parameter μ is known. The quantiles are chosen from a large sample that is either complete or censored (singly-censored or
doubly-censored). The relationship between the proposed test and the asymptotically best linear unbiased estimate (ABLUE)
of the scale parameter is discussed. 相似文献
19.
Miguel A. Arcones 《Annals of the Institute of Statistical Mathematics》2003,55(3):563-583
We study the order of convergence of the Kolmogorov-Smirnov distance for the bootstrap of the mean and the bootstrap of quantiles
when an arbitrary bootstrap sample size is used. We see that for the bootstrap of the mean, the best order of the bootstrap
sample is of the order ofn, wheren is the sample size. In the case of non-lattice distributions and the bootstrap of the sample mean; the bootstrap removes
the effect of the skewness of the distribution only when the bootstrap sample equals the sample size. However, for the bootstrap
of quantiles, the preferred order of the bootstrap sample isn
2/3. For the bootstrap of quantiles, if the bootstrap sample is of ordern
2 or bigger, the bootstrap is not consistent. 相似文献
20.
Improving on the minimum risk equivariant estimator of a location parameter which is constrained to an interval or a half-interval 总被引:3,自引:0,他引:3
Éric Marchand William E. Strawderman 《Annals of the Institute of Statistical Mathematics》2005,57(1):129-143
For location families with densitiesf
0(x−θ), we study the problem of estimating θ for location invariant lossL(θ,d)=ρ(d−θ), and under a lower-bound constraint of the form θ≥a. We show, that for quite general (f
0, ρ), the Bayes estimator δ
U
with respect to a uniform prior on (a, ∞) is a minimax estimator which dominates the benchmark minimum risk equivariant (MRE) estimator. In extending some previous
dominance results due to Katz and Farrell, we make use of Kubokawa'sIERD (Integral Expression of Risk Difference) method, and actually obtain classes of dominating estimators which include, and
are characterized in terms of δ
U
. Implications are also given and, finally, the above dominance phenomenon is studied and extended to an interval constraint
of the form θ∈[a, b].
Research supported by NSERC of Canada. 相似文献