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THE least squares estimator FOR AN ORNSTEIN-UHLENBECK PROCESS DRIVEN BY A HERMITE PROCESS WITH A PERIODIC MEAN

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Acta Mathematica Scientia 2021年第2期41卷 517-534页

作者： Guangjun SHEN Qian YU Zheng TANG Department of Mathematics Anhui Normal UniversityWuhu 241000China School of Statistics East China Normal UniversityShanghai 200062China School of Mathematics and Finance Chuzhou UniverstyChuzhou 239012China

We consider the least square estimator for the parameters of Ornstein-Uhlenbeck processes dY_(s)=(∑_(j=1)^(k)μ_(j)φ_(j)(s)-βY_(s))ds+dZ_(s)^(q,H),driven by the Hermite process Z_(s)^(q,H)with order q≥1 and a Hurst index H∈(1/2,1),where the periodic functionsφ_(j)(s),,j=1,...,κare bounded,and the real numbersμ_(j),,j=1,...,κtogether withβ>0 are unknown *** establish the consistency of a least squares estimation and obtain the asymptotic behavior for the *** also introduce alternative estimators,which can be looked upon as an application of the least squares *** terms of the fractional Ornstein-Uhlenbeck processes with periodic mean,our work can be regarded as its non-Gaussian extension.

关键词： least squares estimator consistency asymptotic distribution Ornstein-Uhlenbeck processes Hermite processes

Approximation to the Distribution of the least squares estimators in Two Dimensional Cosine Models by Randomly Weighted Bootstrap

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Acta Mathematicae Applicatae Sinica 2013年第4期29卷 765-776页

作者： Yuan-yuan ZHAO Rui-xing MING Yao-hua WU Department of Statistics and Finance University of Science and Technology of China School of Mathematical Sciences Nanjing Normal University Institute of Finance and Statistics Nanjing Normal University School of Statistics and Mathematics Zhejiang Gongshang University

Recently, Kundu and Gupta （Metrika, 48：83 C 97, 1998） established the asymptotic normality of the least squares estimators in the two dimensional cosine model. In this paper, we give the approximation to the general least squares estimators by using random weights which is called the Bayesian bootstrap or the random weighting method by Rubin （Annals of Statistics, 9：130 C 134, 1981） and Zheng （Acta Math. Appl. Sinica （in Chinese）, 10（2）： 247 C 253, 1987）. A simulation study shows that this approximation works very well.

关键词： two dimensional model least squares estimator Bayesian bootstrap random weighting method

THE LIMIT THEOREM FOR DEPENDENT RANDOM VARIABLES WITH APPLICATIONS TO AUTOREGRESSION MODELS

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Journal of Systems Science & Complexity 2011年第3期24卷 565-579页

作者： Yong ZHANG Xiaoyun YANG Zhishan DONG Dehui WANG College of Mathematics Jilin University (Qianwei Campus) Changchun 130012 China

This paper studies the autoregression models of order one, in a general time series setting that allows for weakly dependent innovations. Let {Xt} be a linear process defined by Xt =∑k=0^∞ψ kεt-k, where {ψk, k ≥ 0} is a sequence of real numbers and {εk, k = 0, ±1, ±2,...} is a sequence of random variables. Two results are proved in this paper. In the first result, assuming that {εk, k ≥ 1} is a sequence of asymptotically linear negative quadrant dependent （ALNQD） random variables, the authors find the limiting distributions of the least squares estimator and the associated regression t statistic. It is interesting that the limiting distributions are similar to the one found in earlier work under the assumption of i.i.d, innovations. In the second result the authors prove that the least squares estimator is not a strong consistency estimator of the autoregressive parameter a when {εk, k ≥ 1} is a sequence of negatively associated （NA） random variables, and ψ0 = 1, ψk = 0, k ≥ 1.

关键词： ALNQD autoregression models least squares estimator negatively associated unit root test.

least squares ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION

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Acta Mathematica Scientia 2016年第2期36卷 394-408页

作者：申广君尹修伟闫理坦 Department of Mathematics Anhui Normal University Department of Mathematics Donghua University

In this article, we study a least squares estimator （LSE） of θ for the Ornstein- Uhlenbeck process X0=0,dXt=θXtdt＋dBt^ab, t ≥ 0 driven by weighted fractional Brownian motion B^a,b with parameters a, b. We obtain the consistency and the asymptotic distribution of the LSE based on the observation {Xs, s∈[0,t]} as t tends to infinity.

关键词： Weighted fractional Brownian motion least squares estimator Ornstein-Uhl-enbeck process

The Consistency of LSE estimators in Partial Linear Regression Models under Mixing Random Errors

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Acta Mathematica Sinica,English Series 2024年第5期40卷 1244-1272页

作者： Yun Bao YAO Yu Tan LÜ Chao LU Wei WANG Xue Jun WANG School of Mathematical Sciences Anhui UniversityHefei 230601P.R.China School of Big Data and Artificial Intelligence Chizhou UniversityChizhou 247000P.R.China School of Big Data and Statistics Anhui UniversityHefei 230601P.R.China

In this paper,we consider the partial linear regression model y_(i)=x_(i)β^(*)+g(ti)+ε_(i),i=1,2,...,n,where(x_(i),ti)are known fixed design points,g(·)is an unknown function,andβ^(*)is an unknown parameter to be estimated,random errorsε_(i)are(α,β)-mix_(i)ng random *** p-th(p>1)mean consistency,strong consistency and complete consistency for least squares estimators ofβ^(*)and g(·)are investigated under some mild *** addition,a numerical simulation is carried out to study the finite sample performance of the theoretical ***,a real data analysis is provided to further verify the effect of the model.

关键词： (α,β)-mixing random variables partial linear regression model least squares estimator consistency

Asymptotic inference for AR(1) panel data

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Applied Mathematics(A Journal of Chinese Universities) 2020年第3期35卷 265-280页

作者： SHEN Jian-fei PANG Tian-xiao School of Mathematical Sciences Zhejiang UniversityHangzhou 310027China

A general asymptotic theory is given for the panel data AR(1) model with time series independent in different cross sections. The theory covers the cases of stationary process, local to unity process, unit root process, mildly integrated, mildly explosive and explosive processes. It is assumed that the cross-sectional dimension and time-series dimension are respectively N and T. The results in this paper illustrate that whichever the process is, with an appropriate regularization, the least squares estimator of the autoregressive coefficient converges in distribution to a normal distribution with rate at least O(N-1/3). Since the variance is the key to characterize the normal distribution, it is important to discuss the variance of the least squares estimator. We will show that when the autoregressive coefficient ρ satisfies |ρ| 1. ρ = 1 is the critical point where the convergence rate changes radically. The transition process is studied by assuming ρ depending on T and going to 1. An interesting phenomenon discovered in this paper is that, in the explosive case, the least squares estimator of the autoregressive coefficient has a standard normal limiting distribution in the panel data case while it may not has a limiting distribution in the univariate time series case.

关键词： AR(1)model least squares estimator Limiting distribution Non-stationray Panel data

Parameter Estimation for the Discretely Observed Vasicek Model with Small Fractional Lévy Noise

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Acta Mathematica Sinica,English Series 2020年第4期36卷 443-461页

作者： Guang Jun SHEN Qing Bo WANG Xiu Wei YIN Department of Mathematics Anhui Normal UniversityWuhu 241000P.R.China

The statistical inference of the Vasicek model driven by small Levy process has a long *** this paper,we consider the problem of parameter estimation for Vasicek model dX_t=(μ-θX_t)dt+εdL_t^d,t∈[0,1],X_0=x_0,driven by small fractional Lévy noise with the known parameter d less than one half,based on discrete high-frequency observations at regularly spaced time points{t_i=i/n,i=1,2,...,n}.For the general case and the null recurrent case,the consistency as well as the asymptotic behavior of least squares estimation of unknown parametersμandθhave been established as small dispersion coefficientε→0 and large sample size n→∞simultaneously.

关键词： Ornstein–Uhlenbeck process fraction Lévy processes least squares estimator consistency asymptotic distribution

ERRATUM TO： least squares ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION （ACTA MATHEMATICA SCIENTIA 2016,36B （2）：394-408）

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Acta Mathematica Scientia 2017年第4期37卷 1173-1176页

作者：申广君尹修伟闫理坦 Department of Mathematics Anhui Normal University Wuhu 241000 China Department of Mathematics Donghua University Shanghai 201620 China

We give a correction of Theorem 2.2 of Shen, Yin and Yan （2016）.

关键词： weighted fractional Brownian motion least squares estimator Ornstein-Uhlenbeck process

Adaptive Unified Biased estimators of Parameters in Linear Model

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Acta Mathematicae Applicatae Sinica 2004年第3期20卷 425-432页

作者： HuYang Li-xingZhu CollegeofScience ChongqingUniversitychongqing400044China DepartmentofStatisticsandActuarialScience TheUniversityofHongKong

To tackle multi collinearity or ill-conditioned design matrices in linear models, adaptive biased estimators such as the time-honored Stein estimator, the ridge and the principal component estimators have been studied intensively. To study when a biased estimator uniformly outperforms the least squares estimator, some sufficient conditions are proposed in the literature. In this paper, we propose a unified framework to formulate a class of adaptive biased estimators. This class includes all existing biased estimators and some new ones. A sufficient condition for outperforming the least squares estimator is proposed. In terms of selecting parameters in the condition, we can obtain all double-type conditions in the literature.

关键词： least squares estimator linear model sufficient condition adaptive unified biased estimator