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1.
In this paper, we continue the investigation of an estimator proposed in [Yu. Davydov, V. Paulauskas, and A. Račkauskas, More
on p-stable convex sets in Banach spaces, J. Theor. Probab., 13:39–64, 2000] and [V. Paulauskas, A new estimator for tail index, Acta Appl. Math., 79:55–67, 2003] and considered in [V. Paulauskas and M. Vaičiulis, Once more on comparison of tail index estimators, preprint, 2010]. We propose a class of modifications of the so-called DPR estimator and demonstrate that these modifications can have better
asymptotic properties than the original DPR estimator. 相似文献
2.
Mamikon S. Ginovyan 《Acta Appl Math》2011,115(2):233-254
The paper considers a problem of construction of asymptotically efficient estimators for functionals defined on a class of
spectral densities, and bounding the minimax mean square risks. We define the concepts of H- and IK-efficiency of estimators, based on the variants of Hájek-Ibragimov-Khas’minskii convolution theorem and Hájek-Le
Cam local asymptotic minimax theorem, respectively, and show that the simple “plug-in” statistic Φ(I
T
), where I
T
=I
T
(λ) is the periodogram of the underlying stationary Gaussian process X(t) with an unknown spectral density θ(λ), λ∈ℝ, is H- and IK-asymptotically efficient estimator for a linear functional Φ(θ), while for a nonlinear smooth functional Φ(θ) an H- and IK-asymptotically efficient estimator is the statistic F([^(q)]T)\Phi(\widehat{\theta}_{T}), where [^(q)]T\widehat{\theta}_{T} is a suitable sequence of the so-called “undersmoothed” kernel estimators of the unknown spectral density θ(λ). Exact asymptotic bounds for minimax mean square risks of estimators of linear functionals are also obtained. 相似文献
3.
P. Kabaila 《Acta Appl Math》2007,96(1-3):283-291
Suppose that Y
1 and Y
2 are independent and have Binomial(n
1,p
1) and Binomial (n
2,p
2) distributions respectively. Also suppose that θ=p
1−p
2 is the parameter of interest. We consider the problem of finding an exact confidence limit (either upper or lower) for θ. The solution to this problem is very important for statistical practice in the health and life sciences. The ‘tail method’
provides a solution to this problem. This method finds the exact confidence limit by exact inversion of a hypothesis test
based on a specified test statistic. Buehler (J. Am. Stat. Assoc.
52, 482–493, 1957) described, for the first time, a finite-sample optimality property of this confidence limit. Consequently,
this confidence limit is sometimes called a Buehler confidence limit. An early tail method confidence limit for θ was described by Santner and Snell (J. Am. Stat. Assoc.
75, 386–394, 1980) who used the maximum likelihood estimator of θ as the test statistic. This confidence limit is known to be very inefficient (see e.g. Cytel Software, StatXact, version
6, vol. 2, 2004). The efficiency of the confidence limit resulting from the tail method depends greatly on the test statistic
on which it is based. We use the results of Kabaila (Stat. Probab. Lett.
52, 145–154, 2001) and Kabaila and Lloyd (Aust. New Zealand J. Stat.
46, 463–469, 2004, J. Stat. Plan. Inference
136, 3145–3155, 2006) to provide a detailed explanation for the dependence of this efficiency on the test statistic. We consider
test statistics that are estimators, Z-statistics and approximate upper confidence limits. This explanation is used to find
the situations in which the tail method exact confidence limits based on test statistics that are estimators or Z-statistics
are least efficient. 相似文献
4.
M. N. M. van Lieshout 《Annals of the Institute of Statistical Mathematics》2006,58(2):235-259
We propose a new summary statistic for marked point patterns. The underlying principle is to compare the distance from a marked
point to the nearest other marked point in the pattern to the same distance seen from an arbitrary point in space. Information
about the range of interaction can be inferred, and the statistic is well-behaved under random mark allocation. We develop
a range of Hanisch style kernel estimators to tackle the problems of exploding tail variance earlier associated with J-function plug-in estimators, and carry out an exploratory analysis of a forestry data set. 相似文献
5.
Povilas Banys 《Lithuanian Mathematical Journal》2011,51(3):303-309
In [V. Paulauskas, On Beveridge–Nelson decomposition and limit theorems for linear random fields, J. Multivariate Anal., 101:621–639, 2010], limit theorems for linear random fields generated by independent identically distributed innovations
were proved. In this paper, we present the central limit theorem for linear random fields with martingale-differences innovations
satisfying the central limit theorem from [J. Dedecker, A central limit theorem for stationary random fields, Probab. Theory Relat. Fields, 110(3):397–426, 1998] and arranged in lexicographical order. 相似文献
6.
In [V. Paulauskas, On Beveridge–Nelson decomposition and limit theorems for linear random fields, J. Multivariate Anal., 101:621–639, 2010], limit theorems for linear random fields generated by independent identically distributed innovations
were proved. In this paper, which can be regarded as a continuation of the above-mentioned paper, CLT for sums of linear random
field are proved in the case where innovations form martingale differences on the plane (that can be defined in several ways).
In both papers, the so-called Beveridge–Nelson decomposition is used. 相似文献
7.
Panayiotis Bobotas George Iliopoulos Stavros Kourouklis 《Annals of the Institute of Statistical Mathematics》2012,64(2):343-357
We describe a simple approach for estimating the ratio ρ = σ
2/σ
1 of the scale parameters of two populations from a decision theoretic point of view. We show that if the loss function satisfies
a certain condition, then the estimation of ρ reduces to separately estimating σ
2 and 1/σ
1. This implies that the standard estimator of ρ can be improved by just employing an improved estimator of σ
2 or 1/σ
1. Moreover, in the case where the loss function is convex in some function of its argument, we prove that such improved estimators
of ρ are further dominated by corresponding ones that use all the available data. Using this result, we construct new classes
of double-adjustment improved estimators for several well-known convex as well as non-convex loss functions. In particular,
Strawderman-type estimators of ρ in general models are given whereas Shinozaki-type estimators of the ratio of two normal variances are briefly treated. 相似文献
8.
In statistics of extremes, inference is often based on the excesses over a high random threshold. Those excesses are approximately
distributed as the set of order statistics associated to a sample from a generalized Pareto model. We then get the so-called
“maximum likelihood” estimators of the tail index γ. In this paper, we are interested in the derivation of the asymptotic distributional properties of a similar “maximum likelihood”
estimator of a positive tail index γ, based also on the excesses over a high random threshold, but with a trial of accommodation of bias in the Pareto model underlying
those excesses. We next proceed to an asymptotic comparison of the two estimators at their optimal levels. An illustration
of the finite sample behaviour of the estimators is provided through a small-scale Monte Carlo simulation study.
Research partially supported by FCT/POCTI and POCI/FEDER. 相似文献
9.
The crystallization process is represented here by a generalized Boolean model, whose parameters are usually unknown. A better
understanding of the model may be obtained if we estimate the corresponding parameters. In this paper, we provide non-parametric
estimators for the parameters of the model. Among them, the degree of crystallinity at time t is the probability that an arbitrary point in the space has been captured by a crystal before time t. We estimate it following the Kaplan–Meier approach extended to the context of a Johnson–Mehl incomplete tessellation. Three
estimators are defined, according to the kind of data we dispose. The results are also illustrated by simulations. We also
provide estimators for the parameters describing geometrical aspects of the phenomenon.
相似文献
10.
In this paper, we establish oracle inequalities for penalized projection estimators of the intensity of an inhomogeneous
Poisson process. We study consequently the adaptive properties of penalized projection estimators. At first we provide lower
bounds for the minimax risk over various sets of smoothness for the intensity and then we prove that our estimators achieve
these lower bounds up to some constants. The crucial tools to obtain the oracle inequalities are new concentration inequalities
for suprema of integral functionals of Poisson processes which are analogous to Talagrand's inequalities for empirical processes.
Received: 24 April 2001 / Revised version: 9 October 2002 /
Published online: 15 April 2003
Mathematics Subject Classification (2000): 60E15, 62G05, 62G07
Key words or phrases: Inhomogeneous Poisson process – Concentration inequalities – Model selection – Penalized projection estimator – Adaptive
estimation 相似文献
11.
We study the structure of classifying spaces of Kač-Moody groups from a homotopy theoretic point of view. They behave in
many respects as in the compact Lie group case. The mod p cohomology algebra is noetherian and Lannes'T functor computes the mod p cohomology of classifying spaces of centralizers of elementary abelian p-subgroups. Also, spaces of maps from classifying spaces of finite p-groups to classifying spaces of Kač-Moody groups are described in terms of classifying spaces of centralizers while the classifying
space of a Kač-Moody group itself can be described as a homotopy colimit of classifying spaces of centralizers of elementary
abelian p-subgroups, up to p-completion. We show that these properties are common to a larger class of groups, also including parabolic subgroups of Kač-Moody
groups, and centralizers of finite p-subgroups.
Received: 15 June 2000 / in final form: 20 September 2001 / Published online: 29 April 2002 相似文献
12.
Xue-mei Hu Zhi-zhong Wang Feng Liu 《应用数学学报(英文版)》2008,24(1):99-116
This paper studies estimation and serial correlation test of a semiparametric varying-coefficient partially linear EV model of the form Y = X^Tβ +Z^Tα(T) +ε,ξ = X + η with the identifying condition E[(ε,η^T)^T] =0, Cov[(ε,η^T)^T] = σ^2Ip+1. The estimators of interested regression parameters /3 , and the model error variance σ2, as well as the nonparametric components α(T), are constructed. Under some regular conditions, we show that the estimators of the unknown vector β and the unknown parameter σ2 are strongly consistent and asymptotically normal and that the estimator of α(T) achieves the optimal strong convergence rate of the usual nonparametric regression. Based on these estimators and asymptotic properties, we propose the VN,p test statistic and empirical log-likelihood ratio statistic for testing serial correlation in the model. The proposed statistics are shown to have asymptotic normal or chi-square distributions under the null hypothesis of no serial correlation. Some simulation studies are conducted to illustrate the finite sample performance of the proposed tests. 相似文献
13.
A robustified residual autocorrelation is defined based onL
1-regression. Under very general conditions, the asymptotic distribution of the robust residual autocorrelation is obtained.
A robustified portmanteau statistic is then constructed which can be used in checking the goodness-of-fit of AR(p) models
when usingL
1-norm fitting. Empirical results show thatL
1-norm estimators and the proposed portmanteau statistic are robust against outliers, error distributions, and accuracy for
a given finite sample.
Project supported by the Foundation of State Educational Commission and a research grant from the Doctoral Program Foundation
of China (#97000139). 相似文献
14.
M. Bloznelis 《Lithuanian Mathematical Journal》1997,37(3):207-218
The paper gives estimates of the rate of convergence in the central limit theorems for stochastically continuous cadlag processes
proved recently by Bézandry and Fernique (Ann. Inst H. Poincare,28) and Bloznelis and Paulauskas (to appear inStoch. Proc. Appl.).
Research supported by the SFB 343 at Bielefeld, by a Grant from the Lithuanian Government, and by V.P. Grant 94.
Vilnius University, Naugarduko 24; Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Published
in Lietuvos Matematikos Rinkinys, Vol. 37, No. 3, pp. 280–294, July–September, 1997. 相似文献
15.
Jussi Klemelä 《Probability Theory and Related Fields》2006,134(4):539-564
Estimation of a quadratic functional of a function observed in the Gaussian white noise model is considered. A data-dependent
method for choosing the amount of smoothing is given. The method is based on comparing certain quadratic estimators with each
other. It is shown that the method is asymptotically sharp or nearly sharp adaptive simultaneously for the “regular” and “irregular”
region. We consider lp bodies and construct bounds for the risk of the estimator which show that for p=4 the estimator is exactly optimal and for example when p ∈[3,100], then the upper bound is at most 1.055 times larger than the lower bound. We show the connection of the estimator
to the theory of optimal recovery. The estimator is a calibration of an estimator which is nearly minimax optimal among quadratic
estimators.
Writing of this article was financed by Deutsche Forschungsgemeinschaft under project MA1026/6-2, CIES, France, and Jenny
and AnttiWihuri Foundation. 相似文献
16.
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
17.
Assume that the characteristic indexαof stable distribution satisfies 1<α<2,and that the distribution is symmetrical about its mean.We consider the change point estimators for stable distribution withαor scale parameterβshift.For the one case that mean is a known constant,ifαorβchanges,then density function will change too.To this end,we suppose the kernel estimation for a change point.For the other case that mean is an unknown constant,we suppose to apply empirical characteristic function to estimate the change-point location.In the two cases,we consider the consistency and strong convergence rate of estimators.Furthermore,we consider the mean shift case.If mean changes,then corresponding characteristic function will change too.To this end,we also apply empirical characteristic function to estimate change point.We obtain the similar convergence rate.Finally,we consider its application on the detection of mean shift in financial market. 相似文献
18.
Ralf Werner 《Central European Journal of Operations Research》2008,16(2):179-189
It is well known that the robust counterpart introduced by Ben-Tal and Nemirovski (Math Oper Res 23:769–805, 1998) increases
the numerical complexity of the solution compared to the original problem. Kočvara, Nemirovski and Zowe therefore introduced
in Kočvara et al. (Comput Struct 76:431–442, 2000) an approximation algorithm for the special case of robust material optimization,
called cascading. As the title already indicates, we will show that their method can be seen as an adjustment of standard exchange methods
to semi-infinite conic programming. We will see that the adjustment can be motivated by a suitable reformulation of the robust
conic problem.
相似文献
19.
20.
We introduce two residual type a posteriori error estimators for second-order elliptic partial differential equations with its right-hand side in L
p
(1 < p ⩽ 2) space. Both estimators are proved to yield global upper and local lower bounds for the W
1,p
seminorm of the error. We adopt the estimators as the indicators in h-mesh adaptive method to solve two typical model problems. It is verified by the numerical results that the estimators lead
to optimal orders of convergence. 相似文献