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.     

Consistent and asymptotically normal estimators for cyclically time-dependent linear models

We consider a general class of time series linear models where parameters switch according to a known fixed calendar. These parameters are estimated by means of quasi-generalized least squares estimators. conditions for strong consistency and asymptotic normality are given. Applications to cyclical ARMA models with non constant periods are considered.     

(L)2样本深度的基本性质

本文讨论由L^2深度修正得到的L^2深度相应的样本深度的性质，得到了样本深度的相合性和渐近正态性，并证明了它在任意紧集上的一致相合性．最后，基于上述性质简要讨论了样本深度等高的一些性质．     

变系数联立模型的局部线性广义矩变窗宽估计

在随机设计条件下,提出了一类变系数联立模型,运用局部线性广义矩变窗宽估计,对模型的变系数进行了估计,研究了估计量的大样本性质.利用概率论中大数定律和中心极限定理,证明了估计量的大样本性质,局部线性广义矩变窗宽估计具有相合性和渐进正态性.     

ARCH(p)模型样本均值与样本自相关函数的渐近正态性

利用严平稳m步相依序列中心极限定理证明了ARCH(p)模型样本均值与样本自相关函数的渐近正态性质.     

Parametric estimation for simple branching diffusion processes, II

Consider a simple branching diffusion process, which is a branching process in which the individuals move and live and die in space. The offspring distribution has finite moments of all orders. A parametric estimation theory is presented, using time slice data. This involves the use of third order cumulant spectra to identify and estimate the parameters.     

Minimum Distance Estimation in AR(1)-processes

In this paper a new minimum distance estimator is defined in case that the residuals of an AR(1)-process are contaminated normally distributed. This estimator is asymtotically normally distributed and in most cases less biased than the least square estimator. Furthermore, a method is presented to numerically calculate the minimum distance estimator as a root of an implicit function.     

一个简化的新Laplace AR(1)模型 参数估计及其渐近性质

研究了一个简化的新的Laplace AR(1)模型参数的条件最小二乘估计和最大拟似然估计,并讨论了它们的强相合性和渐近正态性.通过数值模拟和实际例子,说明了最大拟似然估计及模型的优越性.     

On uniform asymptotic normality of sequential least squares estimators for the parameters in a stable AR(p)

For a stable autoregressive process of order p with unknown vector parameter θ, it is shown that under a sequential sampling scheme with the stopping time defined by the trace of the observed Fisher information matrix, the least-squares estimator of θ is asymptotically normally distributed uniformly in θ belonging to any compact set in the parameter region.     

Inference for thinned point processes, with application to Cox processes

Given i.i.d. point processes N₁, N₂,…, let the observations be p-thinnings N′₁, N′₂,…, where p is a function from the underlying space E (a compact metric space) to [0, 1], whose interpretation is that a point of N_i at x is retained with probability p(x) and deleted with probability 1−p(x). Strongly consistent estimators of the thinning function p and the Laplace functional L_N(f) = E[e^−N(f)] of the N_i are constructed; associated “central limit” properties are given. Tests are presented, for the case when the N_i and N′_i are both observable, of the hypothesis that the N′_i are p-thinnings of the N_i. State estimation techniques are developed for the case where the N_i are Cox processes directed by unobservable random measures M_i; these techniques yield minimum mean-squared error estimators, based on observation of only the thinned processes N′_i of the N_i and the directing measures M_i. Limit theorems for empirical Laplace functionals of point processes are given.     

Sequential and non-sequential acceptance sampling plans for autocorrelated processes using ARMA(p,q) models

This paper presents variable acceptance sampling plans based on the assumption that consecutive observations on a quality characteristic(X) are autocorrelated and are governed by a stationary autoregressive moving average (ARMA) process. The sampling plans are obtained under the assumption that an adequate ARMA model can be identified based on historical data from the process. Two types of acceptance sampling plans are presented: (1) Non-sequential acceptance sampling: In this case historical data is available based on which an ARMA model is identified. Parameter estimates are used to determine the action limit (k) and the sample size(n). A decision regarding acceptance of a process is made after a complete sample of size n is selected. (2) Sequential acceptance sampling: Here too historical data is available based on which an ARMA model is identified. A decision regarding whether or not to accept a process is made after each individual sample observation becomes available. The concept of Sequential Probability Ratio Test (SPRT) is used to derive the sampling plans. Simulation studies are used to assess the effect of uncertainties in parameter estimates and the effect of model misidentification (based on historical data) on sample size for the sampling plans. Macros for computing the required sample size using both methods based on several ARMA models can be found on the author’s web page .     

双重时序模型矩估计的渐近性：1.样本自协方差（自相关）函数

双重时序模型自提出以来，特别是关于模型的概率性质（如平很快稳性，遍历性）已有许多讨论，但统计推断方面的文章还很少。作为［９，１０］工作的继续，本文及后续文章将讨论矩估计及其大样本性质。首先在本文中，基本的矩估计量（样本自协方差函数及样本自相关函数）的渐近性质对ＡＲ（１）－ＭＡ（ｑ）模型得到讨论，证明了其渐近正态，并 强相合的收敛速度。     

The maximum likelihood estimators in a multivariate normal distribution with AR(1) covariance structure for monotone data

The maximum likelihood estimators are uniquely obtained in a multivariate normal distribution with AR(1) covariance structure for monotone data. The maximum likelihood estimator of mean is unbiased.     

(Almost) matrix‐free solver for piecewise linear functions in abs‐normal form

The abs‐normal form (ANF) is a compact algebraic representation for piecewise linear functions. These functions can be used to approximate piecewise smooth functions and contain valuable information about the nonsmoothness of the investigated function. The information helps to define step directions within general Newton methods that obey the structure of the original function and typically yield better convergence. However, the computation of the generalized Newton directions requires the solution of a piecewise linear equation in ANF. It was observed that the ANF can become very large, even for simple functions. Hence, if a solver is based on the ANF and uses the (Schur‐complement) matrices of the explicit ANF representation, it has to be considered computationally expensive. In this paper, we will address this question and present the first (almost) matrix‐free versions of some solver for ANFs. The theoretical discussion is supported by some numerical run‐time experiments.     

求解病态问题的一种改进的Tikhonov正则化--(1)正则化方法的建立

对于带有右端扰动数据的第一类紧算子方程的病态问题 ,本文应用正则化子建立了一类新的正则化求解方法 ,称之为改进的Tikonov正则化 ;通过适当选取正则参数 ,证明了正则解具有最优的渐近收敛阶 .与通常的Tikhonov正则化相比 ,这种改进的正则化可使正则解取到足够高的最优渐近阶     

Explicit Stationary Distribution of the （L, 1）-reflecting Random Walk on the Half Line

In this paper,we consider the（L,1） state-dependent reflecting random walk（RW） on the half line,which is an RW allowing jumps to the left at a maximal size L.For this model,we provide an explicit criterion for（positive） recurrence and an explicit expression for the stationary distribution.As an application,we prove the geometric tail asymptotic behavior of the stationary distribution under certain conditions.The main tool employed in the paper is the intrinsic branching structure within the（L,1）-random walk.     

Constraint programming for computing non-stationary (R, S) inventory policies

This paper proposes a constraint programming model for computing the finite horizon single-item inventory problem with stochastic demands in discrete time periods with service-level constraints under the non-stationary version of the “periodic review, order-up-to-level” policy (i.e., non-stationary (R, S) or, simply (R_n, S_n)). It is observed that the modeling process is more natural and the required number of variables is smaller compared to the MIP formulation of the same problem. The computational tests show that the CP approach is more tractable than the conventional MIP formulation. Two different domain reduction methods are proposed to improve the computational performance of solution algorithms. The numerical experiments confirmed the effectiveness of these methods.     

Robust goodness-of-fit tests for AR(p) models based onL 1-norm fitting

A robustified residual autocorrelation is defined based onL ₁-regression. Under very general conditions, the asymptotic distribution of the robust residual autocorrelation is obtained. A robustified portmanteau statistic is then constructed which can be used in checking the goodness-of-fit of AR(p) models when usingL ₁-norm fitting. Empirical results show thatL ₁-norm estimators and the proposed portmanteau statistic are robust against outliers, error distributions, and accuracy for a given finite sample. Project supported by the Foundation of State Educational Commission and a research grant from the Doctoral Program Foundation of China (#97000139).