非正则位置参数模型中的拟极大似然估计

当分布密度的形式未知时，参数的极大似然估计没有明确的解析表达式，也不能通过设计算法由计算机运算得到。本文我们将从该分布中抽取的样本当作是来自另一个形式已知的分布密度的样本，该已知分布密度的选取依赖于未知的分布密度，但是具有与未知分布相似的边界性质。基于这两个分布族，我们提出了拟极大似然估计的概念，同时，对这种拟极大似然估计的渐近性质进行了讨论。结果表明拟极大拟然估计与极大似然估计有关相同的渐近性质，并且由于拟极大似然估计的获得不依赖于未知分布密度的形式，只与一已知的分布密度有关，使得通过计算机可以实现对其的求解。     

拟似然非线性模型中MQLE的弱相合性的充分条件

拟似然非线性模型包括广义线性模型作为一个特殊情形.给出了拟似然非线性模型中极大拟似然估计的弱相合性的一些充分条件,其中矩的条件要弱于文献中极大拟似然估计的强相合性的条件.     

多维GARCH模型的半参数有效估计

多元GARCH模型的估计一般采用拟极大似然法(quasi maximum likehood),对于这种方法估计的相合性及渐近正态性已经被很多学者证实,然而对于新息列的分布不是多元正态时,这种估计的有效性还没人研究,本文从拟极大似然估计得到的参数相合估计入手,提出用非参数方法估计多元新息列的分布.     

一类线性结构模型参数的极大似然估计及拟极大似然估计的渐近性质

不少作者探讨过参数的极大似然估计(以下简记为 MLE)的渐近性质.一些统计工作者还把极大似然估计方法用于估计部分参数.即在参数为θ=(θ′_1,θ′_2)′的模型中,当不易求出θ的 MLE,而我们的目的是估计 θ_2时,可将似然函数中其余的参数θ_1用它们的估计(?)来代替,然后极大化这个经代换后的似然函数来求得 θ_2的估计.这就是所谓拟极大似然估计(以下简记为 PMLE).     

受控两性分枝过程相关参数的极大似然估计

本文主要研究了受控两性分枝过程相关参数的极大似然估计,运用极大似然法研究了它的概率分布、控制参数、后代均值和方差.     

一类加权可靠指数分布

本文研究了一种含有形状参数和尺度参数的加权可靠性指数分布.利用变量替换以及极大似然法,研究了在特定尺度参数下此分布的构造性表示,并导出了计算该分布两个参数极大似然估计的迭代解,同时还给出了估计参数的渐近分布形式.     

Lomax分布极大似然估计的两点研究

本文研究了Lomax分布参数极大似然估计的存在性和估计量的收敛性问题.利用严格的分析法和中心极限定理,获得了Lomax分布极大似然估计的存在性和估计量的渐近正态分布的结果,进一步推广到了有缺失数据的两个Lomax总体中,参数的极大似然估计有强相合性和渐近正态性.     

带有Markov型误差的线性模型的假设检验（英文）

本文研究线性模型中关于误差Markov链齐次性的假设检验问题.利用关于未知参数的拟极大似然估计和鞅差方法,获得了似然比检验统计量的极限分布.     

单参数指数分布产品截尾样本场合简单步进应力加速寿命试验损伤失效率模型下的统计分析

本文给出单参数指数分布产品截尾样本场合简单步进应力加速寿命试验损伤失效率模型下参数的极大似然估计和拟矩估计。     

二项线性随机效应模型的拟蒙特卡罗估计

讨论了如何运用拟蒙特卡罗方法对二项线性随机效应模型进行参数估计.首先写出观测数据的边缘对数似然函数,然后用拟蒙特卡罗方法将函数中的积分写成求和的形式,接着利用Newton-Raphson算法计算参数的极大似然估计.以一组种子数据为例,说明该方法是简单可行的.     

Preliminary test estimation for spectra

For a general non-Gaussian stationary linear process, quasi-maximum likelihood estimation of a subset of the parameters of the spectral density is considered when the complementary subset is suspected to be superfluous. A preliminary test quasi-maximum likelihood estimator (q-MLE) of parameters is introduced and, in the light of its mean square error, is compared with the restricted and unrestricted q-MLE.     

B-splines and discretization in an inverse problem for Poisson processes

Recent results on quasi-maximum likelihood histogram sieve estimators in inverse problems for Poisson processes are generalized to B-spline sieves. The impact of discretization effects on strong L² consistency and convergence rates are studied in detail. In particular, a “rates saturation effect”, caused by discretization, is demonstrated. Finite-sample implementation is proposed and tested in a Monte Carlo experiment with the Wicksell problem, which shows a superior performance of the new approach, when compared to other methods commonly used in that context. The proposed algorithm can also be used in cases with only approximately known folding kernel.     

A note on statistical analysis of factor models of high dimension

Science China Mathematics - Linear factor models are familiar tools used in many fields. Several pioneering literatures established foundational theoretical results of the quasi-maximum likelihood...     

Non-Gaussian quasi-likelihood estimation of SDE driven by locally stable Lévy process

We address estimation of parametric coefficients of a pure-jump Lévy driven univariate stochastic differential equation (SDE) model, which is observed at high frequency over a fixed time period. It is known from the previous study (Masuda, 2013) that adopting the conventional Gaussian quasi-maximum likelihood estimator then leads to an inconsistent estimator. In this paper, under the assumption that the driving Lévy process is locally stable, we extend the Gaussian framework into a non-Gaussian counterpart, by introducing a novel quasi-likelihood function formally based on the small-time stable approximation of the unknown transition density. The resulting estimator turns out to be asymptotically mixed normally distributed without ergodicity and finite moments for a wide range of the driving pure-jump Lévy processes, showing much better theoretical performance compared with the Gaussian quasi-maximum likelihood estimator. Extensive simulations are carried out to show good estimation accuracy. The case of large-time asymptotics under ergodicity is briefly mentioned as well, where we can deduce an analogous asymptotic normality result.     

基于ARFIMA-GARCH模型的混成检验

本文研究了ARFIMA-GARCH模型的混成检验问题.基于拟极大指数似然估计,给出了平方残差自相关函数的渐近性,进而建立了基于平方残差自相关函数的混成检验统计量.通过实例分析,表明可利用基于平方残差自相关函数的混成检验统计量来诊断检验由拟极大指数似然估计方法拟合的ARFIMA-GARCH模型.     

Quasi-likelihood analysis for nonsynchronously observed diffusion processes

We consider nonsynchronous sampling of parameterized stochastic regression models, which contain stochastic differential equations. Constructing a quasi-likelihood function, we prove that the quasi-maximum likelihood estimator and the Bayes type estimator are consistent and asymptotically mixed normal when the sampling frequency of the nonsynchronous data becomes large.     

Normal mixture quasi maximum likelihood estimation for non-stationary TGARCH(1,1) models

Although quasi maximum likelihood estimator based on Gaussian density (G-QMLE) is widely used to estimate GARCH-type models, it does not perform successfully when error distribution is either skewed or leptokurtic. This paper proposes normal mixture quasi-maximum likelihood estimator (NM-QMLE) for non-stationary TGARCH(1,1) models. We show that, under mild regular conditions, there is no consistent estimator for the intercept, and the proposed estimator for any other parameter is consistent.     

Quasi-maximum likelihood estimation for multiple volatility shifts

We propose the Gaussian quasi-maximum likelihood estimator (QMLE) to detect and locate multiple volatility shifts. Our Gaussian QMLE is shown to be consistent under suitable conditions and the rate of convergence is provided. It is also shown that the binary segmentation procedure provides a consistent estimation for the number of volatility shifts.     

Quasi-maximum likelihood estimators in generalized linear models with autoregressive processes

The paper studies a generalized linear model(GLM)y_t = h(x_t~T β) + ε_t,t = l,2,...,n,where ε_1 = η_1,ε_1 =ρε_t +η_t,t = 2,3,...;n,h is a continuous differentiable function,η_t'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.     

Estimating parameters in one-way analysis of covariance model with short-tailed symmetric error distributions

We consider one-way analysis of covariance (ANCOVA) model with a single covariate when the distribution of error terms are short-tailed symmetric. The maximum likelihood (ML) estimators of the parameters are intractable. We, therefore, employ a simple method known as modified maximum likelihood (MML) to derive the estimators of the model parameters. The method is based on linearization of the intractable terms in likelihood equations. Incorporating these linearizations in the maximum likelihood, we get the modified likelihood equations. Then the MML estimators which are the solutions of these modified equations are obtained. Computer simulations were performed to investigate the efficiencies of the proposed estimators. The simulation results show that the proposed estimators are remarkably efficient compared with the conventional least squares (LS) estimators.