共查询到20条相似文献,搜索用时 31 毫秒
1.
This paper studies maximum likelihood estimation for a parameterised elliptic diffusion in a manifold. The focus is on asymptotic properties of maximum likelihood estimates obtained from continuous time observation. These are well known when the underlying manifold is a Euclidean space. However, no systematic study exists in the case of a general manifold. The starting point is to write down the likelihood function and equation. This is achieved using the tools of stochastic differential geometry. Consistency, asymptotic normality and asymptotic optimality of maximum likelihood estimates are then proved, under regularity assumptions. Numerical computation of maximum likelihood estimates is briefly discussed. 相似文献
2.
For continuous boundary data, including data of polynomial growth, modified Poisson integrals are used to write solutions to the half space Dirichlet and Neumann problems in Rn. Pointwise growth estimates for these integrals are given and the estimates are proved sharp in a strong sense. For decaying data, a new type of modified Poisson integral is introduced and used to develop asymptotic expansions for solutions of these half space problems. 相似文献
3.
We present a statistical process depending on a continuous time parameter τ whose each margin provides a Generalized Hill’s estimator. In this paper, the asymptotic normality of the finite-dimensional
distributions of this family are completely characterized for τ > 1/2 when the underlying distribution function lies on the maximum domain of attraction. The ratio of two different margins
of the statistical process characterizes entirely the whole domain of attraction. Its asymptotic normality is also studied.
The results permit in general to build a new family of estimators for the extreme value index whose asymptotic properties
can be easily derived. For example, we give a new estimate of the Weibull extreme value index and we study its consistency
and its asymptotic normality.
相似文献
4.
Raymond J Carroll 《Journal of multivariate analysis》1978,8(3):361-371
The asymptotic distribution of multivariate M-estimates is studied. It is shown that, in general, consistency leads to asymptotic normality and a Law of the Iterated Logarithm. The results are used to compute via matrix derivatives the asymptotic distribution of a class of estimates due to Maronna. 相似文献
5.
A. Pérez-González J. M. Vilar-Fernández W. González-Manteiga 《Annals of the Institute of Statistical Mathematics》2009,61(1):85-109
The main objective of this work is the nonparametric estimation of the regression function with correlated errors when observations
are missing in the response variable. Two nonparametric estimators of the regression function are proposed. The asymptotic
properties of these estimators are studied; expresions for the bias and the variance are obtained and the joint asymptotic
normality is established. A simulation study is also included. 相似文献
6.
本文用[1]发展的计数过程去研究截断样本下强率函数核估计的渐进正态性.在弱于[7]和[10]的条件下,得到了更一般的结果.接着我们将这种方法运用到密度函数核估计,在较弱的条件下,得到了截断样本下密度函数核估计的渐进正态性. 相似文献
7.
Rainer Dahlhaus 《Stochastic Processes and their Applications》1985,19(1):135-149
Using convolution properties of frequency-kernels and their upper bounds we obtain some new upper bounds for the cumulants of time series statistics. From these results we derive the asymptotic normality of some spectral estimates and the tightness of tapered empirical spectral functions in the space of Lipschitz-continuous functions. It follows that tapering increases the asymptotic variance of the estimates by a constant factor. All results are proved under integrability conditions on the spectra. A functional limit theorem for the empirical spectral function is also given without assuming all moments of the underlying process to exist. 相似文献
8.
Shaul K. Bar-Lev 《Annals of the Institute of Statistical Mathematics》1984,36(1):217-222
Summary Consider a truncated exponential family of absolutely continuous distributions with natural parameter θ and truncation parameter
γ. Strong consistency and asymptotic normality are shown to hold for the maximum likelihood and maximum conditional likelihood
estimates of θ with γ unknown. Moreover, these two estimates are also shown to have the same limiting distribution, coinciding
with that of the maximum likelihood estimate for θ when γ is assumed to be known. 相似文献
9.
Location and scale parameters are estimated via “window estimates”. The consistency and asymptotic normality of the estimates are established. The special case of the Cauchy distribution is considered, where the estimates are shown to have the same asymptotic distribution as the maximum-likelihood estimates. Additional applications are given for the Pearson type-VII distributions. The estimates have the advantages of ease of computation and high asymptotic efficiencies for certain heavy-tailed distributions. 相似文献
10.
研究了随机截尾情形下Rayleigh分布参数的最大似然估计,研究了最大似然估计的存在唯一性;在很一般的条件下证明了估计的强、弱相合性和渐近正态性. 相似文献
11.
《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(3-4):207-226
In the present paper, a framework for parametric estimation in nonlinear time series is developed. Strong consistency and asymptotic normality of minimum Hellinger distance estimates for a determined class of nonlinear models are investigated. The main Interest for these estimates is motivated by their robustness under perturbations as it has been emphazized in Beran [2]. The first part of the paper is devoted to the study of some probabilistic properties which ensure the existence and the optimal properties of the estimates 相似文献
12.
Ya. M. Chabanyuk 《Ukrainian Mathematical Journal》2006,58(12):1916-1923
We consider the asymptotic normality of a continuous procedure of stochastic approximation in the case where the regression
function contains a singularly perturbed term depending on the external medium described by a uniformly ergodic Markov process.
Within the framework of the scheme of diffusion approximation, we formulate sufficient conditions for asymptotic normality
in terms of the existence of a Lyapunov function for the corresponding averaged equation.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 12, pp. 1686–1692, December, 2006. 相似文献
13.
《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(2-3):107-118
A recursive stochastic optimization procedure under dependent disturbances is studied. It is based on the Polyak-Ruppert algorithm with trajectory averaging. Almost sure convergence of the algorithm is proved as well as asymptotic normality of the delivered estimates. It is shown that the presented algorithm attains the highest possible asymptotic convergence rate for stochastic approximation algorithms 相似文献
14.
研究了α-混合样本下最近邻密度估计的渐近性质,证明了估计的渐近正态性并且给出了其渐近方差的显式表达式,由此构造了α-混合样本下概率密度的渐近置信区间. 相似文献
15.
Fixed design regression for time series: Asymptotic normality 总被引:1,自引:0,他引:1
Consider the fixed regression model with general weights, and suppose that the error random variables are coming from a strictly stationary stochastic process, satisfying the strong mixing condition. The asymptotic normality of the proposed estimate is established under weak conditions. The applicability of the results obtained is demonstrated by way of two existing estimates, the Gasser-Müller estimate and that of Priestley and Chao. The asymptotic normality of these estimates is further illustrated by means of a concrete example from the class of autoregressive processes. 相似文献
16.
Yu. N. Lin'kov 《Journal of Mathematical Sciences》1991,53(4):409-415
We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987. 相似文献
17.
We consider the linear regression model in the case when the independent variables are measured with errors, while the variances
of the main observations depend on an unknown parameter. In the case of normally distributed replicated regressors we propose
and study new classes of two-step estimates for the main unknown parameter. We find consistency and asymptotic normality conditions
for first-step estimates and an asymptotic normality condition for second-step estimates. We discuss conditions under which
these estimates have the minimal asymptotic variance. 相似文献
18.
Summary An estimator of the asymptotic variance of (a randomly stopped) linear combination of a function of order statistics is considered and its asymptotic normality is studied under appropriate regularity conditions. A comparative study of the regularity conditions pertaining to the asymptotic normality and strong convergence of linear combinations of functions of order statistics and their estimated asymptotic variances is also made.Research supported by the Office of Naval Research under ONR Contract N00014-79-C-0522This research is dedicated to Professor Leopold Schmetterer on the occasion of his 60th birthday 相似文献
19.
We propose a class of robust estimates for multivariate linear models. Based on the approach of MM-estimation (Yohai 1987, [24]), we estimate the regression coefficients and the covariance matrix of the errors simultaneously. These estimates have both a high breakdown point and high asymptotic efficiency under Gaussian errors. We prove consistency and asymptotic normality assuming errors with an elliptical distribution. We describe an iterative algorithm for the numerical calculation of these estimates. The advantages of the proposed estimates over their competitors are demonstrated through both simulated and real data. 相似文献
20.
Rainer Dahlhaus 《Journal of multivariate analysis》1985,16(3):412-431
The asymptotic normality of some spectral estimates, including a functional central limit theorem for an estimate of the spectral distribution function, is proved for fourth-order stationary processes. In contrast to known results it is not assumed that all moments exist or that the process is linear. The data are allowed to be tapered. Using some recent results on the central limit theorem for stationary processes, corollaries are obtained for strong and φ-mixing sequences and linear transformations of martingale differences. 相似文献