共查询到20条相似文献,搜索用时 15 毫秒
1.
Theoretical and Mathematical Physics - Non-Gaussianity is an important resource for quantum information processing with continuous variables. We introduce a measure of the non-Gaussianity of... 相似文献
2.
《Statistics & probability letters》2001,53(3):305-314
The present paper deals with the statistical inference of the simultaneous switching autoregressive (SSAR) model. This model has been introduced by Kunitomo and Sato (Jpn. Econ. Rev. 50 (2) (1996) 161) in order to take into account the asymmetry in financial and economical time series modelling. Under some conditions which ensure some probabilistic properties of the model, we establish, under other mild assumptions, the asymptotic properties of the minimum Hellinger distance estimates of the parameters. An application to a true data is also given. 相似文献
3.
Lucien Birgé 《Probability Theory and Related Fields》1986,71(2):271-291
Résumé On s'intéresse ici aux possibles vitesses d'estimation d'une densité à support compact dans
m
sous des hypothèses de régularité, lorsque la perte est mesurée par le carré de la distance de Hellinger (on regardera aussi le cas connu des normes
pour 1q2) et le risque est le risque minimax sur la famille. On donne une méthode générale permettant de traiter les problèmes dans le cadre de la théorie de l'approximation sous des conditions concernant l'entropie métrique et l' -capacité des familles à estimer. Les rapports entre régularité et entropie métrique étant bien connus, nous pourrons aussi traiter les cas classiques et d'autres qui le sont moins. Sous des conditions de bornes inférieures les vitesses sont celles observées pour la norme
mais elles diffèrent dans le cas général. On montre aussi que les restrictions sur la compacité du support ou la régularité sont indispensables et que leur absence mène à l'impossibilité d'obtenir une estimation raisonnable en ce sens que n'importe quelle suite d'estimateurs sera arbitrairement mauvaise en un point au moins. Un résultat analogue est vrai sous des conditions de régularité.
This work was carried out during a visit of the author at the Mathematical Sciences Research Institute at Berkeley 相似文献
This work was carried out during a visit of the author at the Mathematical Sciences Research Institute at Berkeley 相似文献
4.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(7):2373-2381
Common remainder is significant to the estimation of the robust Chinese Remainder Theorem (CRT). This paper presents two optimal estimates of common remainder for the robust CRT. The two different optimal estimates are obtained based on different definitions of circular distance. Both of the two estimations are more effective with lower computational complexity than the existing searching method. Simulation results show that the two estimations have nearly the same performance, however, the second optimal estimation has less computation than the first one. These optimal estimates can improve the performance of the estimation of the robust CRT. 相似文献
5.
We investigate the estimation problem of parameters in a two-sample semiparametric model. Specifically, let X1,…,Xn be a sample from a population with distribution function G and density function g. Independent of the Xi’s, let Z1,…,Zm be another random sample with distribution function H and density function h(x)=exp[α+r(x)β]g(x), where α and β are unknown parameters of interest and g is an unknown density. This model has wide applications in logistic discriminant analysis, case-control studies, and analysis of receiver operating characteristic curves. Furthermore, it can be considered as a biased sampling model with weight function depending on unknown parameters. In this paper, we construct minimum Hellinger distance estimators of α and β. The proposed estimators are chosen to minimize the Hellinger distance between a semiparametric model and a nonparametric density estimator. Theoretical properties such as the existence, strong consistency and asymptotic normality are investigated. Robustness of proposed estimators is also examined using a Monte Carlo study. 相似文献
6.
Our interest is in the problem where independent samples are drawn from two different discrete populations, possibly with a common parameter. The goal is to test hypothesis about the parameters involved in these two samples. A number of tests are developed for the above purpose based on the Hellinger distance and penalized versions of it. The asymptotic distributions of the test statistics are derived. Extensive simulation results are provided, which illustrate the theory developed and the robustness of the methods. 相似文献
7.
V. N. Solev 《Journal of Mathematical Sciences》2007,145(2):4923-4930
In the paper, we consider the estimation problem for an unknown density on independent observations. We use the minimum distance
estimation method. It is shown that the accuracy of estimation is connected with the rate of increase of the entropy of the
parametrical set. Bibliography: 9 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 339, 2006, pp. 151–162. 相似文献
8.
Information criteria are applied for estimation of random vectors. Normal random vectors and random vectors with an unknown distribution are considered. Both linear estimates and estimates represented by a measurable function of observations are derived.Translated from Vychislitel'naya i Prildadnaya Matematika, No. 62, pp. 105–113, 1987. 相似文献
9.
This paper studies the asymptotic behavior of the minimum Hellinger distance estimator of the underlying parameter in a supercritical branching process whose offspring distribution is known to belong to a parametric family. This estimator is shown to be asymptotically normal, efficient at the true model and robust against gross errors. These extend the results of Beran (Ann. Statist. 5, 445–463 (1977)) from an i.i.d., continuous setup to a dependent, discrete setup. 相似文献
10.
Practically all organizations seek to create value by selecting and executing portfolios of actions that consume resources. Typically, the resulting value is uncertain, and thus organizations must take decisions based on ex ante estimates about what this future value will be. In this paper, we show that the Bayesian modeling of uncertainties in this selection problem serves to (i) increase the expected future value of the selected portfolio, (ii) raise the expected number of selected actions that belong to the optimal portfolio ex post, and (iii) eliminate the expected gap between the realized ex post portfolio value and the estimated ex ante portfolio value. We also propose a new project performance measure, defined as the probability that a given action belongs to the optimal portfolio. Finally, we provide analytic results to determine which actions should be re-evaluated to obtain more accurate value estimates before portfolio selection. In particular, we show that the optimal targeting of such re-evaluations can yield a much higher portfolio value in return for the total resources that are spent on the execution of actions and the acquisition of value estimates. 相似文献
11.
In this Note, we determine the minimum Hellinger distance estimate of an ARFIMA (AutoRegressive Fractionally Integrated Moving Average) process. The estimate minimizes the Hellinger distance between the probability density function of the innovation of the process and a parameterized random function. Under some assumptions, we establish the asymptotic properties of this estimate. 相似文献
12.
Efficient robust estimates in parametric models 总被引:1,自引:0,他引:1
Rudolf Beran 《Probability Theory and Related Fields》1981,55(1):91-108
Summary Let {P
n
:}, an open subset ofR
k
, be a regular parametric model for a sample ofn independent, identically distributed observations. This paper describes estimates {T
n
;n1} of which are asymptotically efficient under the parametric model and are robust under small deviations from that model. In essence, the estimates are adaptively modified, one-step maximum likelihood estimates, which adjust themselves according to how well the parametric model appears to fit the data. When the fit seems poor,T
n
discounts observations that would have large influence on the value of the usual one-step MLE. The estimates {T
n
} are shown to be asymptotically minimax, in the Hájek-LeCam sense, for a Hellinger ball contamination model. An alternative construction of robust asymptotically minimax estimates, as modified MLE's, is described for canonical exponential families.This research was supported in part by National Science Foundation Grant MCS 75-10376 相似文献
13.
14.
15.
Constantine A. Drossos Andreas N. Philippou 《Annals of the Institute of Statistical Mathematics》1980,32(1):121-123
It is shown that minimum distance estimates enjoy the invariance property of maximum likelihood estimates.
Supported under Grant No. 18-2773 of the American University of Beirut. 相似文献
16.
Choung Min Ng Seng-Huat Ong H.M. Srivastava 《Applied Mathematical Modelling》2013,37(12-13):7374-7385
Maximum likelihood (ML) estimation is a popular method for parameter estimation when modeling discrete or count observations but unfortunately it may be sensitive to outliers. Alternative robust methods like minimum Hellinger distance (MHD) have been proposed for estimation. However, in the multivariate case, the MHD method leads to computer intensive estimation especially when the joint probability density function is complicated. In this paper, a Hellinger type distance measure based on the probability generating function is proposed as a tool for quick and robust parameter estimation. The proposed method yields consistent estimators, performs well for simulated and real data, and can be computationally much faster than ML or MHD estimation. 相似文献
18.
Efficiency and robustness are two essential concerns on statistical estimation. Unfortunately, it was widely accepted that there existed a contradiction between achieving efficiency and robustness simultaneously. For parametric models with complete data, the minimum Hellinger distance estimation introduced by Beran (Ann Stat 5:445–463, 1977) has been shown that it can reconcile this contradiction. Because data in biostatistics, actuarial science or economics are often subject to censoring and even involve a fraction of long-term survivors, our study aims to extend the minimum Hellinger distance estimation to a two-sample semiparametric cure rate model with right-censored survival data. The asymptotic properties such as consistency, efficiency, normality, and robustness of the proposed estimator have been considered and its performances are examined via simulation studies in comparison with those of the maximum semiparametric conditional likelihood estimator introduced by Shen et al. (J Am Stat Assoc 102:1235–1244, 2007). Finally, our method is illustrated by analyzing a real data set: Bone Marrow Transplant Data. 相似文献
19.
V. M. Zolotarev 《Journal of Mathematical Sciences》1992,59(4):921-925
Translated from:Problemy Ustoichivosti Stokhasticheskikh Modelei, Trudy Seminara, 1989, pp. 55–59. 相似文献