Asymptotically Optimal Empirical Bayes Estimation of Parameter for Scale-exponential Family under PA Samples

The Bayes estimator of the parameter is obtained for the scale exponential family in the case of identically distributed and positively associated（PA） samples under weighted square loss function.We construct the empirical Bayes（EB） estimator and prove it is asymptotic optimal.

ASYMPTOTICALLY OPTIMAL EMPIRICAL BAYES ESTIMATION FOR THE PARAMETERS OF MULTI－PARAMETER DISCRETE EXPONENTIAL FAMILY

For the multi-parameter discrete exponential family,we construct an empirical Bayes(EB)estimator of the vector-valued parameterθ.under some conditions,this estimator is proved to be asymptotically optimal.

An Approach to Dynamic Asymptotic Estimation for Hurst Index of Network Traffic

As an important parameter to describe the sudden nature of network traffic, Hurst index typically conducts behaviors of both self-similarity and long-range dependence. With the evolution of network traffic over time, more and more data are generated. Hurst index estimation value changes with it, which is strictly consistent with the asymptotic property of long-range dependence. This paper presents an approach towards dynamic asymptotic estimation for Hurst index. Based on the calculations in terms of the incremental part of time series, the algorithm enjoys a considerable reduction in computational complexity. Moreover, the local sudden nature of network traffic can be readily captured by a series of real-time Hurst index estimation values dynamically. The effectiveness and tractability of the proposed approach are demonstrated through the traffic data from OPNET simulations as well as real network, respectively.

Asymptotically Optimal and Admissible Empirical Bayes Estimation of Normal Parameter

Under square loss, this paper constructs the empirical Bayes（EB） estimation for the parameter of normal distribution which has both asymptotic optimality and admissibility. Moreover, the convergence rate of the EB estimation obtained is proved to be O（n^-1）.

Asymptotic normality of error density estimator in stationary and explosive autoregressive models

In this paper,we consider the limit distribution of the error density function estima-tor in the rst-order autoregressive models with negatively associated and positively associated random errors.Under mild regularity assumptions,some asymptotic normality results of the residual density estimator are obtained when the autoregressive models are stationary process and explosive process.In order to illustrate these results,some simulations such as con dence intervals and mean integrated square errors are provided in this paper.It shows that the residual density estimator can replace the density\estimator"which contains errors.

Nonparametric Estimation of the Trend Function for Stochastic Processes Driven by Fractional Brownian Motion of the Second Kind

The present paper deals with the problem of nonparametric kernel density estimation of the trend function for stochastic processes driven by fractional Brownian motion of the second kind.The consistency,the rate of convergence,and the asymptotic normality of the kernel-type estimator are discussed.Besides,we prove that the rate of convergence of the kernel-type estimator depends on the smoothness of the trend of the nonperturbed system.

调和分数Ornstein-Uhlenbeck金融模型的参数估计

为了描述金融资产价格过程的长相依性和自相似性,首先构建由调和分数布朗运动驱动的分数Ornstein-Uhlenbeck(O-U)模型.由于调和分数布朗运动是分数布朗运动的推广,故所构建的模型具有更广泛的应用.然后基于离散观测样本,利用最小二乘方法,得到模型漂移参数的估计量,并证明了估计量的相合性和渐近分布.最后,通过模拟展示了所得估计量的有限样本性质,模拟结果显示估计量的值拟合参数真值的效果较好.

Estimation for constant-stress accelerated life test from generalized half-normal distribution

In the constant-stress accelerated life test, estimation issues are discussed for a generalized half-normal distribution under a log-linear life-stress model. The maximum likelihood estimates with the corresponding fixed point type iterative algorithm for unknown parameters are presented, and the least square estimates of the parameters are also proposed. Meanwhile, confidence intervals of model parameters are constructed by using the asymptotic theory and bootstrap technique. Numerical illustration is given to investigate the performance of our methods.

Parameter Estimation for Complex Ornstein-Uhlenbeck Processes

The drift parameter estimation problem of the complex Ornstein-Uhlenbeck process driven by a complexα-stable motion is considered.Based on discrete observations,an estimator of the unknown drift parameter is constructed by using the least squares method.Moreover,the strong consistency and the asymptotic distribution of the least squares estimator are derived under some assumptions.

PARAMETER ESTIMATION FOR A CLASS OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY SMALL STABLE NOISES FROM DISCRETE OBSERVATIONS

We study the least squares estimation of drift parameters for a class of stochastic differential equations driven by small a-stable noises, observed at n regularly spaced time points ti = i/n, i = 1,...,n on [0, 1]. Under some regularity conditions, we obtain the consistency and the rate of convergence of the least squares estimator （LSE） when a small dispersion parameter ε→0 and n →∞ simultaneously. The asymptotic distribution of the LSE in our setting is shown to be stable, which is completely different from the classical cases where asymptotic distributions are normal.

ASYMPTOTIC PROPERTY STUDY OF THE LEAST SQUARE ESTIMATES OF 2-D EXPONENTIAL SIGNALS VIA COMPLEX SIGNAL PROCESSING APPROACH

By use of the approach of complex random signal processing, the asymptotic statistical properties of the least square estimates of 2-D exponential signals are studied. In doing so it is found that the representation is considerably more intuitive, and is analytically more tractable.

ON BAHADUR-TYPE ASYMPTOTIC EFFICIENCY OF POINT ESTIMATORS UNDER IRREGULAR TRUNCATED DISTRIBUTION FAMILY

In this paper, the optimal convergence rates of point estimators have been found under the irregular truncated distribution family, and corresponding Bahadurtype asymptotic efficiencies have been established. It has beed justified that commonly used estimators are all efficient in this sense.

ASYMPTOTIC NORMALITY OF WAVELET ESTIMATOR IN HETEROSCEDASTIC REGRESSION MODEL

The following heteroscedastic regression model Yi = g（xi） ＋σiei （1 ≤i ≤ n） is 2 considered, where it is assumed that σi^2 = f（ui）, the design points （xi,ui） are known and nonrandom, g and f are unknown functions. Under the unobservable disturbance ei form martingale differences, the asymptotic normality of wavelet estimators of g with f being known or unknown function is studied.

Parameter Estimation for Constantinides-Ingersoll Model from Discrete Observations

The parameter estimation problem for an economic model called Constantinides-Ingersoll model is investigated based on discrete observations. Euler-Maruyama scheme and iterative method are applied to getting the joint conditional probability density function. The maximum likelihood technique is employed for obtaining the parameter estimators and the explicit expressions of the estimation error are given. The strong consistency properties of the estimators are proved by using the law of large numbers for martingales and the strong law of large numbers. The asymptotic normality of the estimation error for the diffusion parameter is obtained with the help of the strong law of large numbers and central-limit theorem. The simulation for the absolute error between estimators and true values is given and the hypothesis testing is made to verify the effectiveness of the estimators.

From Nonparametric Density Estimation to Parametric Estimation of Multidimensional Diffusion Processes

The paper deals with the estimation of parameters of multidimensional diffusion processes that are discretely observed. We construct estimator of the parameters based on the minimum Hellinger distance method. This method is based on the minimization of the Hellinger distance between the density of the invariant distribution of the diffusion process and a nonparametric estimator of this density. We give conditions which ensure the existence of an invariant measure that admits density with respect to the Lebesgue measure and the strong mixing property with exponential rate for the Markov process. Under this condition, we define an estimator of the density based on kernel function and study his properties (almost sure convergence and asymptotic normality). After, using the estimator of the density, we construct the minimum Hellinger distance estimator of the parameters of the diffusion process and establish the almost sure convergence and the asymptotic normality of this estimator. To illustrate the properties of the estimator of the parameters, we apply the method to two examples of multidimensional diffusion processes.

Some Asymptotic Properties for Multivariate Partially Linear Models

The paper considers a multivariate partially linear model under independent errors,and investigates the asymptotic bias and variance-covariance for parametric component βand nonparametric component F（·）by the GJS estimator and Kernel estimation.

Hazard Rate Function Estimation Using Weibull Kernel

In this paper, we define the Weibull kernel and use it to nonparametric estimation of the probability density function (pdf) and the hazard rate function for independent and identically distributed (iid) data. The bias, variance and the optimal bandwidth of the proposed estimator are investigated. Moreover, the asymptotic normality of the proposed estimator is investigated. The performance of the proposed estimator is tested using simulation study and real data.

THE CONSISTENCY AND ASYMPTOTIC NORMALITY OF NEAREST NEIGHBOR DENSITY ESTIMATOR UNDER α-MIXING CONDITION

We investigate the consistency and asymptotic normality of nearest-neighbor density estimator of a sample data process based on α-mixing assumption. We extend the correspondent result under independent identical cases.

LIMITING BEHAVIOR OF RECURSIVE M-ESTIMATORS IN MULTIVARIATE LINEAR REGRESSION MODELS AND THEIR ASYMPTOTIC EFFICIENCIES

Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.

THE NONPARAMETRIC ESTIMATION OF THE NEXT FAILURE TIME

The nonparametric estimation of the next failure time is considered in this paper. The estimator given in the paper has a.s. convergence under some proper conditions. The asymptotic normality of the estimator is also discussed.