共查询到4条相似文献,搜索用时 0 毫秒
1.
Frank Marohn 《Annals of the Institute of Statistical Mathematics》1997,49(4):645-666
This paper deals with the estimation of the extreme value index in local extreme value models. We establish local asymptotic normality (LAN) under certain extreme value alternatives. It turns out that the central sequence occurring in the LAN expansion of the likelihood process is up to a rescaling procedure the Hill estimator. The central sequence plays a crucial role for the construction of asymptotic optimal statistical procedures. In particular, the Hill estimator is asymptotically minimax. 相似文献
2.
In this paper, we consider a multidimensional diffusion process with jumps whose jump term is driven by a compound Poisson
process. Let a(x,θ) be a drift coefficient, b(x,σ) be a diffusion coefficient respectively, and the jump term is driven by a Poisson random measure p. We assume that its intensity measure qθ has a finite total mass. The aim of this paper is estimating the parameter α = (θ,σ) from some discrete data. We can observe
n + 1 data at tin = ihn,
. We suppose hn → 0, nhn → ∞, nhn2 → 0.
Final version 20 December 2004 相似文献
3.
Alan F. Karr 《Journal of multivariate analysis》1985,16(3):368-392
Given i.i.d. point processes N1, N2,…, let the observations be p-thinnings N′1, N′2,…, where p is a function from the underlying space E (a compact metric space) to [0, 1], whose interpretation is that a point of Ni at x is retained with probability p(x) and deleted with probability 1−p(x). Strongly consistent estimators of the thinning function p and the Laplace functional LN(f) = E[e−N(f)] of the Ni are constructed; associated “central limit” properties are given. Tests are presented, for the case when the Ni and N′i are both observable, of the hypothesis that the N′i are p-thinnings of the Ni. State estimation techniques are developed for the case where the Ni are Cox processes directed by unobservable random measures Mi; these techniques yield minimum mean-squared error estimators, based on observation of only the thinned processes N′i of the Ni and the directing measures Mi. Limit theorems for empirical Laplace functionals of point processes are given. 相似文献
4.
Kernel type density estimators are studied for random fields. It is proved that the estimators are asymptotically normal if
the set of locations of observations become more and more dense in an increasing sequence of domains. It turns out that in
our setting the covariance structure of the limiting normal distribution can be a combination of those of the continuous parameter
and the discrete parameter cases. The proof is based on a new central limit theorem for α-mixing random fields. Simulation
results support our theorems.
Final version 29 October 2004 相似文献