Rate of strong consistency of the maximum quasi-likelihood estimator in quasi-likelihood nonlinear models

Quasi-likelihood nonlinear models （QLNM） include generalized linear models as a special case. Under some regularity conditions, the rate of the strong consistency of the maximum quasi-likelihood estimation （MQLE） is obtained in QLNM. In an important case, this rate is O（n-^1/2（loglogn）^1/2）, which is just the rate of LIL of partial sums for i.i.d variables, and thus cannot be improved anymore.

Asymptotic Normality of Multi-Dimension Quasi Maximum Likelihood Estimate in Generalized Linear Models withAdaptive Design

We study the quasi likelihood equation in Generalized Linear Models（GLM） with adaptive design ∑（i=1）^n xi（yi-h（x＇iβ））=0, where yi is a q=vector, and xi is a p×q random matrix. Under some assumptions, it is shown that the Quasi- Likelihood equation for the GLM has a solution which is asymptotic normal.

Estimating Equations for Estimation of Mcdonald Generalized Beta— Binomial Parameters

There has been a considerable recent attention in modeling over dispersed binomial data occurring in toxicology, biology, clinical medicine, epidemiology and other similar fields using a class of Binomial mixture distribution such as Beta Binomial distribution (BB) and Kumaraswamy-Binomial distribution (KB). A new three-parameter binomial mixture distribution namely, McDonald Generalized Beta Binomial (McGBB) distribution has been developed which is superior to KB and BB since studies have shown that it gives a better fit than the KB and BB distribution on both real life data set and on the extended simulation study in handling over dispersed binomial data. The dispersion parameter will be treated as nuisance in the analysis of proportions since our interest is in the parameters of McGBB distribution. In this paper, we consider estimation of parameters of this MCGBB model using Quasi-likelihood (QL) and Quadratic estimating functions (QEEs) with dispersion. By varying the coefficients of the QEE’s we obtain four sets of estimating equations which in turn yield four sets of estimates. We compare small sample relative efficiencies of the estimates based on QEEs and quasi-likelihood with the maximum likelihood estimates. The comparison is performed using real life data sets arising from alcohol consumption practices and simulated data. These comparisons show that estimates based on optimal QEEs and QL are highly efficient and are the best among all estimates investigated.

Parameter Estimation for the NEAR(p) Model

As to the acronym NEAR（p）, it means “New Exponential Autoregressive Process of order p”. The NEAR（p） model is defined by

长记忆时间序列的均值单变点估计

文章采用拟极大似然法估计了一类长记忆时间序列模型的单均值变点,在变点大小固定和变点收缩两种情形下分析了估计量的渐近性质。研究发现,变点大小与长记忆性之间存在一种权衡关系。具体而言,当变点大小固定时,变点估计量是不相合的,而变分点估计量是T-相合的;当变点收缩时,变点估计量的收敛速度依赖于记忆参数d,估计量的极限分布得以推导。最后,蒙特卡洛实验和实证分析验证了所提理论结果的有限样本表现。

On some problems of weak consistency of quasi-maximum likelihood estimates in generalized linear models

In this paper,we explore some weakly consistent properties of quasi-maximum likelihood estimates(QMLE) concerning the quasi-likelihood equation in=1 Xi(yi-μ(Xiβ)) = 0 for univariate generalized linear model E(y |X) = μ(X'β).Given uncorrelated residuals {ei = Yi-μ(Xiβ0),1 i n} and other conditions,we prove that βn-β0 = Op(λn-1/2) holds,where βn is a root of the above equation,β0 is the true value of parameter β and λn denotes the smallest eigenvalue of the matrix Sn = ni=1 XiXi.We also show that the convergence rate above is sharp,provided independent non-asymptotically degenerate residual sequence and other conditions.Moreover,paralleling to the elegant result of Drygas(1976) for classical linear regression models,we point out that the necessary condition guaranteeing the weak consistency of QMLE is Sn-1→ 0,as the sample size n →∞.

Quasi-Maximum Likelihood Estimators in Generalized Linear Models with Autoregressive Processes

The paper studies a generalized linear model（GLM）yt = h（xt^T β） ＋ εt,t = l,2,...,n,where ε1 = η1,ε1 =ρεt ＋ηt,t = 2,3,...;n,h is a continuous differentiable function,ηt＇s are independent and identically distributed random errors with zero mean and finite variance σ^2.Firstly,the quasi-maximum likelihood（QML） estimators of β,p and σ^2 are given.Secondly,under mild conditions,the asymptotic properties（including the existence,weak consistency and asymptotic distribution） of the QML estimators are investigated.Lastly,the validity of method is illuminated by a simulation example.

Efficiency of Some Estimators for a Generalized Poisson Autoregressive Process of Order 1

Various models have been proposed in the literature to study non-negative integer-valued time series. In this paper, we study estimators for the generalized Poisson autoregressive process of order 1, a model developed by Alzaid and Al-Osh [1]. We compare three estimation methods, the methods of moments, quasi-likelihood and conditional maximum likelihood and study their asymptotic properties. To compare the bias of the estimators in small samples, we perform a simulation study for various parameter values. Using the theory of estimating equations, we obtain expressions for the variance-covariance matrices of those three estimators, and we compare their asymptotic efficiency. Finally, we apply the methods derived in the paper to a real time series.

Adaptive quasi-likelihood estimate in generalized linear models

This paper gives a thorough theoretical treatment on the adaptive quasilikelihood estimate of the parameters in the generalized linear models. The unknown covariance matrix of the response variable is estimated by the sample. It is shown that the adaptive estimator defined in this paper is asymptotically most efficient in the sense that it is asymptotic normal, and the covariance matrix of the limit distribution coincides with the one for the quasi-likelihood estimator for the case that the covariance matrix of the response variable is completely known.

带固定效应空间自回归面板模型的参数估计及检验

研究带固定效应空间自回归面板模型的拟极大似然估计和检验问题.首先通过矩阵变换消除模型中的固定效应项,给出参数的拟极大似然估计,并且建立参数估计的渐近性质.此外,还基于矩阵变换,针对空间自回归系数λ构造LM检验统计量来检验是否显著不为0,推导出该统计量在零假设下的渐近分布.最后通过模拟研究结果证实参数估计及LM检验的有限样本性质,展示提出的估计和检验方法是可行有效的.

Strong consistency of maximum quasi-likelihood estimates in generalized linear models

In a generalized linear model with q × 1 responses, bounded and fixed p × qregressors Zi and general link function, under the most general assumption on the mini-mum eigenvalue of∑ni＝1n ZiZ'i, the moment condition on responses as weak as possibleand other mild regular conditions, we prove that with probability one, the quasi-likelihoodequation has a solutionβn for all large sample size n, which converges to the true regres-sion parameterβo. This result is an essential improvement over the relevant results in literature.

Estimation of Treatment Effects in Nonlinear Models with Unobserved Confounding

Estimation of treatment effects is one of the crucial mainstays in economics and sociology studies.The problem will become more serious and complicated if the treatment variable is endogenous for the presence of unobserved confounding.The estimation and conclusion are likely to be biased and misleading if the endogeny of treatment variable is ignored.In this article,we propose the pseudo maximum likelihood method to estimate treatment effects in nonlinear models.The proposed method allows the unobserved confounding and random error terms to exist in an arbitrary relationship(such as,add or multiply),and the unobserved confounding have different influence directions on treatment variables and outcome variables.The proposed estimator is consistent and asymptotically normally distributed.Simulation studies show that the proposed estimator performs better than the special regression estimator,and the proposed method is stable for various distribution of error terms.Finally,the proposed method is applied to the real data that studies the influence of individuals have health insurance on an individual’s decision to visit a doctor.

Asymptotic normality and strong consistency of maximum quasi-likelihood estimates in generalized linear models

In a generalized linear model with q × 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ∑ni=1 ZiZ'i, the moment condition on responses as weak as possible and the other mild regular conditions, we prove that the maximum quasi-likelihood estimates for the regression parameter vector are asymptotically normal and strongly consistent.

ASYMPTOTIC NORMALITY OF QUASI MAXIMUM LIKELIHOOD ESTIMATE IN GENERALIZED LINEAR MODELS

For the Generalized Linear Model (GLM), under some conditions including that the specification of the expectation is correct, it is shown that the Quasi Maximum Likelihood Estimate (QMLE) of the parameter-vector is asymptotic normal. It is also shown that the asymptotic covariance matrix of the QMLE reaches its minimum (in the positive-definte sense) in case that the specification of the covariance matrix is correct.

Consistency and Asymptotic Normality of the Maximum Quasi-likelihood Estimator in Quasi-likelihood Nonlinear Models with Random Regressors

This paper proposes some regularity conditions, which result in the existence, strong consistency and asymptotic normality of maximum quasi-likelihood estimator （MQLE） in quasi-likelihood nonlinear models （QLNM） with random regressors. The asymptotic results of generalized linear models （GLM） with random regressors are generalized to QLNM with random regressors.

ASYMPTOTIC NORMALITY OF MAXIMUM QUASI-LIKELIHOOD ESTIMATORS IN GENERALIZED LINEAR MODELS WITH FIXED DESIGN

在有固定设计的概括线性模型，在假设和另外的整齐条件下面，最大的伪可能性评估者的 asymptotic 规度，是有自然连接功能的伪可能性方程的根，被获得，在的地方表示最小的特征值， X i 是围住的p ×& #8201 ； q 退回 ors ，和 y i 是q ×& #8201 ； 1 回答。

Strong Consistency of Maximum Quasi-Likelihood Estimator in Quasi-Likelihood Nonlinear Models

This paper proposes some regularity conditions. On the basis of the proposed regularity conditions, we show the strong consistency of maximum quasi-likelihood estimation （MQLE） in quasi-likelihood nonlinear models （QLNM）. Our results may be regarded as a further generalization of the relevant results in Ref. [4].

信息不对称下成交量与波动率关系建模与统计推断

本文首次提出信息不对称背景下成交量和波动率关系的日度完备模型。新模型假设当日成交量和已实现测度为次日隐信息流带来新信息,而隐信息流驱动知情交易者交易。基于此模型,本文给出时间序列平稳遍历性成立的充分条件,并且运用高斯拟极大似然法,建立模型参数估计的渐近理论,模拟研究验证了渐近理论的正确性。本文将新模型应用于中国沪深A股市场、美国纽交所和纳斯达克市场的大型公司。基于全样本的模型拟合结果发现:成交量的放大将导致次日条件波动率增大,而条件波动率的增大伴随着成交量的放大,同时,大部分个股中存在信息交易;在存续时间长、市值靠前且交易活跃的中国个股中,相较于基准波动率模型——已实现GARCH模型,新模型大多具有更好的样本内拟合能力;而在市值靠前且交易活跃的美股中,新模型的表现并不优于已实现GARCH模型。在滚动窗口的波动率预测上,较其他被广泛使用的已有模型,新模型在本文研究的中国个股中普遍具有更好的表现;而在本文研究的美股中,已实现GARCH模型表现较好。这反映了新模型更加适用于存续时间长、市值靠前且交易活跃的中国股票市场数据。

非零均值噪声下ARMA-GARCH模型的拟极大似然估计

ARMA-GARCH模型在金融领域已得到广泛应用,可以用来研究金融资产价格的变化情况.对金融资产收益率建模时,通常假设噪声服从高斯分布.然而,实际研究表明,金融资产收益率可能具有正向或负向阶段性跳跃特征.对于此类金融数据,基于高斯分布的ARMA-GARCH模型在预测效果上显得不足.因此,研究了非零均值噪声扰动下的ARMA-GARCH模型,证明了拟极大似然估计量(QMLE)的强相合性和渐近正态性.进一步,通过数值模拟和实证分析说明了该模型的有效性.