共查询到20条相似文献,搜索用时 15 毫秒
1.
Xia Chen 《Probability Theory and Related Fields》2000,116(1):89-123
Let {X
n
}
n
≥0 be a Harris recurrent Markov chain with state space E and invariant measure π. The law of the iterated logarithm and the law of weak convergence are given for the additive functionals
of the form
where ƒ is a real π-centered function defined on E. Some similar results are also obtained for additive functionals which are martingales associated with {X
n
}
n
≥0.
Received: 15 September 1998 / Revised version: 1 April 1999 相似文献
2.
We study the maximum likelihood estimator for stochastic equations with additive fractional Brownian sheet. We use the Girsanov
transform for the the two-parameter fractional Brownian motion, as well as the Malliavin calculus and Gaussian regularity
theory.
相似文献
3.
We consider a process given by the SDE , t∈[0,T), with initial condition , where T∈(0,∞], α∈R, (Bt)t∈[0,T) is a standard Wiener process, b:[0,T)→R?{0} and σ:[0,T)→(0,∞) are continuously differentiable functions. Assuming , t∈[0,T), with some K∈R, we derive an explicit formula for the joint Laplace transform of and for all t∈[0,T) and for all α∈R. Our motivation is that the maximum likelihood estimator (MLE) of α can be expressed in terms of these random variables. As an application, we show that in case of α=K, K≠0,
4.
A Maximum A Posteriori (MAP) estimator for trajectories of diffusions observed via a noisy non-linear sensor, defined in [1] for diffusions evolving in "flat" spaces, is extended to arbitrary nondegenerate diffusions in W (subject to some technical constraints). An existence theorem for the MAP trajectories estimator is proved. Finally, relations between the trajectories MAP estimator and the pointwise MAP estimator are demonstrated. Some open problems concerning the issue of finite dimensionality of the MAP trajectories estimator are pointed out 相似文献
5.
The problem of estimating the boundary of a uniform distribution on a disc is considered when data are measured with normally distributed additive random error. The problem is solved in two steps. In the first step the domain is subdivided into thin slices and the endpoints of slices are obtained within the framework of a corresponding one-dimensional problem. For the estimations implemented in that step the moment method and the maximum likelihood method are used. As there are numerical problems with calculating the variance of the estimator in the maximum likelihood approach, its good approximation is also given. 相似文献
6.
Frank van der Meulen Moritz Schauer 《Stochastics An International Journal of Probability and Stochastic Processes》2018,90(5):641-662
We present a general framework for Bayesian estimation of incompletely observed multivariate diffusion processes. Observations are assumed to be discrete in time, noisy and incomplete. We assume the drift and diffusion coefficient depend on an unknown parameter. A data-augmentation algorithm for drawing from the posterior distribution is presented which is based on simulating diffusion bridges conditional on a noisy incomplete observation at an intermediate time. The dynamics of such filtered bridges are derived and it is shown how these can be simulated using a generalised version of the guided proposals introduced in Schauer, Van der Meulen and Van Zanten (2017, Bernoulli 23(4A)). 相似文献
7.
吴黎明 《应用数学学报(英文版)》2000,16(2):149-161
1.IntroductionandMainResultsAssumethat(Xt),.T(T~NorAl)isaPolishspaceE-valuedMarkovprocess,definedon(fi,F,(R),(ot),(P-c)..E),withitssemigroupoftransitionkernels(Pt).Here(ot)isthesemigroupofshiftsonfisuchthatX.(otw)~X. t(w),Vs,tET;(R)isthenaturalfiltration.Throughoutthispaperweassumethat(Pt)issymmetricandergodicwithrespectto(w.r.t.forshort)aprobabilitymeasurepon(E,e)(eistheBorela--fieldofE),i.e.,.Symmetry:(Ptf,g)~(f,Pig):~isfptgdp,acET,if,gCL'(P);.ErgodicitytFOranyfEL'(P),ifPtf~f… 相似文献
8.
Helmut Strasser 《Journal of multivariate analysis》1975,5(2):206-226
Let (X, ) be a measurable space, Θ ? an open interval and PΩ ∥ , Ω ? Θ, a family of probability measures fulfilling certain regularity conditions. Let be the maximum likelihood estimate for the sample size n. Let λ be a prior distribution on Θ and let be the posterior distribution for the sample size n given . denotes a loss function fulfilling certain regularity conditions and Tn denotes the Bayes estimate relative to λ and L for the sample size n. It is proved that for every compact K ? Θ there exists cK ≥ 0 such that This theorem improves results of Bickel and Yahav [3], and Ibragimov and Has'minskii [4], as far as the speed of convergence is concerned. 相似文献
9.
J. Beirlant A. Berlinet G. Biau 《Annals of the Institute of Statistical Mathematics》2008,60(3):651-677
The symmetric derivative of a probability measure at a Lebesgue point can often be specified by an exact relation involving
a regularity index. Knowledge of this index is of practical interest, for example to specify the local behavior of the measure
under study and to evaluate bandwidths or number of neighbors to take into account in smoothing techniques. This index also
determines local rates of convergence of estimators of particular points of curves and surfaces, like minima and maxima. In
this paper, we consider the estimation of the d-dimensional regularity index. We introduce an estimator and derive the basic asymptotic results. Our estimator is inspired
by an estimator proposed in Drees and Kaufmann (1998, Stochastic Processes and their Applications, 75, 149–172) in the context of extreme value statistics. Then, we show how (estimates of) the regularity index can be used to
solve practical problems in nearest neighbor density estimation, such as removing bias or selecting the number of neighbors.
Results of simulations are presented. 相似文献
10.
We use Nummelin splitting in continuous time in order to prove laws of iterated logarithm for additive functionals of a Harris recurrent Markov process, with deterministic or random renormalization. 相似文献
11.
In a sequence ofn independent random variables the pdf changes fromf(x, 0) tof(x, 0 + δvn−1) after the firstnλ variables. The problem is to estimateλ (0, 1 ), where 0 and δ are unknownd-dim parameters andvn → ∞ slower thann1/2. Letn denote the maximum likelihood estimator (mle) ofλ. Analyzing the local behavior of the likelihood function near the true parameter values it is shown under regularity conditions that ifnn2(− λ) is bounded in probability asn → ∞, then it converges in law to the timeT(δjδ)1/2 at which a two-sided Brownian motion (B.M.) with drift1/2(δ′Jδ)1/2ton(−∞, ∞) attains its a.s. unique minimum, whereJ denotes the Fisher-information matrix. This generalizes the result for small change in mean of univariate normal random variables obtained by Bhattacharya and Brockwell (1976,Z. Warsch. Verw. Gebiete37, 51–75) who also derived the distribution ofTμ forμ > 0. For the general case an alternative estimator is constructed by a three-step procedure which is shown to have the above asymptotic distribution. In the important case of multiparameter exponential families, the construction of this estimator is considerably simplified. 相似文献
12.
The rate of convergence in a sample path sense is given for a strongly consistent, recursive estimator. This estimator is for the unknown average return rate of the risky asset that is a parameter in a bilinear stochastic differential equation for the wealth in a portfolio selection and consumption model.This research was partially supported by NSF Grant No. ECS-84-03286-A01 and by University of Kansas General Research Allocation No. 3806-XO-0038. 相似文献
13.
本文研究了连续时间下非参数回归的误差官度估计的收敛速度,给出了一定条件下误差密度的估计量^fT(x)的均方收敛速度,详细说明了以下重要结果:E[^fT(x)-f(x)]^2=O(T^-1/4)其中f(x)表示误差过程{et,t≥0}的未知密度。 相似文献
14.
考虑了NSD误差下的线性模型并建立回归参数LAD估计的线性表示.这些结果将独立误差的情形推广和改进到NSD误差的情形.作为一个应用,获得了LAD估计量的收敛率. 相似文献
15.
Chin-Tsang Chiang Mei-Cheng Wang 《Annals of the Institute of Statistical Mathematics》2009,61(1):197-213
This article mainly considers the recurrent event process with independent censoring mechanism through a more flexible varying-coefficient
model. The smoothing estimators for the varying-coefficient functions are also proposed via maximizing the kernel weight version
of the log-partial likelihood function with respect to the coefficients at each time point. For the selection of appropriate
bandwidths and the construction of confidence intervals, the consistent empirical smoothing estimators for the covariance
functions of the estimators and a bias correction method are considered. As for the baseline effect function of recurrent
events in the population, two different smoothing estimation methods are suggested and investigated. In this study, the asymptotic
properties of the proposed smoothing estimators are derived. The finite sample properties of our methods are examined through
a Monte Carlo simulation. Moreover, the procedures are applied to a recurrent sample of AIDS link to intravenous experiences
(ALIVE) cohort study. 相似文献
16.
Éric Marchand François Perron 《Annals of the Institute of Statistical Mathematics》2009,61(1):215-234
For the problem of estimating under squared error loss the parameter of a symmetric distribution which is subject to an interval
constraint, we develop general theory which provides improvements on various types of inadmissible procedures, such as maximum
likelihood procedures. The applications and further developments given include: (i) symmetric location families such as the
exponential power family including double-exponential and normal, Student and Cauchy, a Logistic type family, and scale mixture
of normals in cases where the variance is lower bounded; (ii) symmetric exponential families such as those related to a Binomial(n,p) model with bounded |p−1/2| and to a Beta(α + θ, α −θ) model; and (iii) symmetric location distributions truncated to an interval (−c,c). Finally, several of the dominance results are studied with respect to model departures yielding robustness results, and
specific findings are given for scale mixture of normals and truncated distributions.
Research supported by NSERC of Canada. 相似文献
17.
Anders Rygh Swensen 《Stochastic Processes and their Applications》1985,19(1):111-123
Some optimal inference results for a class of diffusion processes, including the continuous state branching process and the approximate Wright-Fisher model with selection, are derived.It is then showed how the theory of convergence of experiments, due to Le Cam, can be applied to derive corresponding results for processes approximating these diffusions. 相似文献
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20.
Hui Jiang 《Journal of Mathematical Analysis and Applications》2011,382(1):367-382
In the present paper, we study the asymptotic behavior for estimator of the drift parameter in an Ornstein-Uhlenbeck process. The Lr-convergence rate and the precise asymptotics in the law of iterated logarithm and in the law of logarithm for the estimator are obtained. Moreover, we also get the complete moment convergence of this estimator. The main method of this paper is the deviation inequality for the quadratic functional. 相似文献