共查询到20条相似文献,搜索用时 15 毫秒
1.
Asymptotic local equivalence in the sense of Le Cam is established for inference on the drift in multidimensional ergodic
diffusions and an accompanying sequence of Gaussian shift experiments. The nonparametric local neighbourhoods can be attained
for any dimension, provided the regularity of the drift is sufficiently large. In addition, a heteroskedastic Gaussian regression
experiment is given, which is also locally asymptotically equivalent and which does not depend on the centre of localisation.
For one direction of the equivalence an explicit Markov kernel is constructed. 相似文献
2.
Summary. We establish that a non-Gaussian nonparametric regression model is asymptotically equivalent to a regression model with Gaussian
noise. The approximation is in the sense of Le Cam's deficiency distance Δ; the models are then asymptotically equivalent
for all purposes of statistical decision with bounded loss. Our result concerns a sequence of independent but not identically
distributed observations with each distribution in the same real-indexed exponential family. The canonical parameter is a
value f(t
i
) of a regression function f at a grid point t
i
(nonparametric GLM). When f is in a H?lder ball with exponent we establish global asymptotic equivalence to observations of a signal Γ(f(t)) in Gaussian white noise, where Γ is related to a variance stabilizing transformation in the exponential family. The result
is a regression analog of the recently established Gaussian approximation for the i.i.d. model. The proof is based on a functional
version of the Hungarian construction for the partial sum process.
Received: 4 February 1997 相似文献
3.
Nakahiro Yoshida 《Probability Theory and Related Fields》1992,92(3):275-311
Summary The asymptotic expansions of the probability distributions of statistics for the small diffusion are derived by means of the Malliavin calculus. From this the second order efficiency of the maximum likelihood estimator is proved.The research was supported in part by Grant-in-Aid for Encouragement of Young Scientists from the Ministry of Education, Science and Culture 相似文献
4.
The article is devoted to the nonparametric estimation of the quadratic covariation of non-synchronously observed Itô processes in an additive microstructure noise model. In a high-frequency setting, we aim at establishing an asymptotic distribution theory for a generalized multiscale estimator including a feasible central limit theorem with optimal convergence rate on convenient regularity assumptions. The inevitably remaining impact of asynchronous deterministic sampling schemes and noise corruption on the asymptotic distribution is precisely elucidated. A case study for various important examples, several generalizations of the model and an algorithm for the implementation warrant the utility of the estimation method in applications. 相似文献
5.
Nakahiro Yoshida 《Probability Theory and Related Fields》1993,95(4):429-450
Summary Using the Malliavin calculus we derived asymptotic expansion of the distributions of the Bayes estimators for small diffusions. The second order efficiency of the Bayes estimator is proved. 相似文献
6.
Summary Given a collection of nested closed, convex symmetric sets and a linear functional, we find estimates which are within a logarithm term of being simultaneously asymptotically minimax. Moreover, these estimates can be constructed so that the loss of this logarithm term only occurs on a small subset of functions. These estimates are quasi-optimal since there do not exist estimators which do not lose a logarithm term on some part of the parameter spaces.This author was partially supported by an NSF Grant DMS-9123956This author was supported by an NSF Postdoctoral Research Fellowship 相似文献
7.
8.
The theory of Gaussian graphical models is a powerful tool for independence analysis between continuous variables. In this framework, various methods have been conceived to infer independence relations from data samples. However, most of them result in stepwise, deterministic, descent algorithms that are inadequate for solving this issue. More recent developments have focused on stochastic procedures, yet they all base their research on strong a priori knowledge and are unable to perform model selection among the set of all possible models. Moreover, convergence of the corresponding algorithms is slow, precluding applications on a large scale. In this paper, we propose a novel Bayesian strategy to deal with structure learning. Relating graphs to their supports, we convert the problem of model selection into that of parameter estimation. Use of non-informative priors and asymptotic results yield a posterior probability for independence graph supports in closed form. Gibbs sampling is then applied to approximate the full joint posterior density. We finally give three examples of structure learning, one from synthetic data, and the two others from real data. 相似文献
9.
U. Stadtmüller 《Periodica Mathematica Hungarica》1986,17(2):83-108
We consider a class of nonparametric estimators for the regression functionm(t) in the model:y
i
=m(t
i
) +
i
, 1 i n, t
i
[0, 1], which are linear in the observationsy
i
. Several limit theorems concerning local and global stochastic and a.s. convergence and limit distributions are given. 相似文献
10.
We estimate the drift parameter in a simple linear model driven by fractional Brownian motion. We propose maximum likelihood estimators (MLE) for the drift parameter construct by using a random walk approximation of the fractional Brownian motion. 相似文献
11.
T. Deck 《Journal of multivariate analysis》2006,97(2):563-573
The estimation of a real parameter θ in a linear stochastic differential equation of the simple type is investigated, based on noisy, time continuous observations of Xt. Sufficient conditions on the continuous functions β and σ are given such that the (conditionally normal) Bayes estimators of θ satisfy certain error bounds and are strongly consistent. 相似文献
12.
We establish contiguity of families of probability measures indexed by T, as T → ∞, for classes of continuous time stochastic processes which are either stationary diffusions or Gaussian processes with known covariance. In most cases, and in all the examples we consider in Section 4, the covariance is completely determined by observing the process continuously over any finite interval of time. Many important consequences pertaining to properties of tests and estimators, outlined in Section 5, will then apply. 相似文献
13.
Wiener processes with random effects for degradation data 总被引:12,自引:0,他引:12
Xiao Wang 《Journal of multivariate analysis》2010,101(2):340-351
This article studies the maximum likelihood inference on a class of Wiener processes with random effects for degradation data. Degradation data are special case of functional data with monotone trend. The setting for degradation data is one on which n independent subjects, each with a Wiener process with random drift and diffusion parameters, are observed at possible different times. Unit-to-unit variability is incorporated into the model by these random effects. EM algorithm is used to obtain the maximum likelihood estimators of the unknown parameters. Asymptotic properties such as consistency and convergence rate are established. Bootstrap method is used for assessing the uncertainties of the estimators. Simulations are used to validate the method. The model is fitted to bridge beam data and corresponding goodness-of-fit tests are carried out. Failure time distributions in terms of degradation level passages are calculated and illustrated. 相似文献
14.
We introduce a sequence of stopping times that allow us to study an analogue of a life-cycle decomposition for a continuous time Markov process, which is an extension of the well-known splitting technique of Nummelin to the continuous time case. As a consequence, we are able to give deterministic equivalents of additive functionals of the process and to state a generalisation of Chen’s inequality. We apply our results to the problem of non-parametric kernel estimation of the drift of multi-dimensional recurrent, but not necessarily ergodic, diffusion processes. 相似文献
15.
Admissible prediction problems in finite populations with arbitrary rank under matrix loss function are investigated. For the general random effects linear model, we obtained the necessary and sufficient conditions for a linear predictor of the linearly predictable variable to be admissible in the two classes of homogeneous linear predictors and all linear predictors and the class that contains all predictors, respectively. Moreover, we prove that the best linear unbiased predictors (BLUPs) of the population total and the finite population regression coefficient are admissible under different assumptions of superpopulation models respectively. 相似文献
16.
For a class of non-uniformly ergodic Markov chains (X
n
) satisfying exponential or polynomial beta-mixing, under observations (Y
n
) subject to an IID noise with a positive density, it is shown that wrong initial data is forgotten in the mean total variation
topology, with a certain exponential or polynomial rate. 相似文献
17.
In this paper, we establish an inequality of the characteristic functions for strongly mixing random vectors, by which, an upper bound is provided for the supremum of the absolute value of the difference of two multivariate probability density functions based on strongly mixing random vectors. As its application, we consider the consistency and asymptotic normality of a kernel estimate of a density function under strong mixing. Our results generalize some known results in the literature. 相似文献
18.
J. D. Horton 《Aequationes Mathematicae》1981,22(1):56-63
The existence of a Room square of order 2n is known to be equivalent to the existence of two orthogonal one-factorizations of the complete graph on 2n vertices, where orthogonal means any two one-factors involved have at most one edge in common. DefineR(n) to be the maximal number of pairwise orthogonal one-factorizations of the complete graph onn vertices.The main results of this paper are bounds on the functionR. If there is a strong starter of order 2n–1 thenR(2n) 3. If 4n–1 is a prime power, it is shown thatR(4n) 2n–1. Also, the recursive construction for Room squares, to obtain, a Room design of sidev(u – w) +w from a Room design of sidev and a Room design of sideu with a subdesign of sidew, is generalized to sets ofk pairwise orthogonal factorizations. It is further shown thatR(2n) 2n–3. 相似文献
19.
20.
Jugal Ghorai 《Annals of the Institute of Statistical Mathematics》1980,32(1):341-350
LetX
1,...,X
n
be i.i.d. random variable with a common densityf. Let
be an estimate off(x) based on a complete orthonormal basis {φ
k
:k≧0} ofL
2[a, b]. A Martingale central limit theorem is used to show that
, where
and
. 相似文献