Yule–Walker type estimators in periodic bilinear models: strong consistency and asymptotic normality

This paper studies the covariance structure and the asymptotic properties of Yule–Walker (YW) type estimators for a bilinear time series model with periodically time-varying coefficients. We give necessary and sufficient conditions ensuring the existence of moments up to eighth order. Expressions of second and third order joint moments, as well as the limiting covariance matrix of the sample moments are given. Strong consistency and asymptotic normality of the YW estimator as well as hypotheses testing via Wald’s procedure are derived. We use a residual bootstrap version to construct bootstrap estimators of the YW estimates. Some simulation results will demonstrate the large sample behavior of the bootstrap procedure.     

On the calculations of the maximum likelihood estimates for the polynomial spline regression model with unknown knots and AR(1) errors

Asymptotic distributions of the maximum likelihood estimators of the regression coefficients and knot points for the polynomial spline regression models with unknown knots and AR(1) errors have been derived by Chan (1989). Chan showed that under some mild conditions the maximum likelihood estimators, after suitable standardization, asymptotically follow normal distributions as n diverges to infinity. For the calculations of the maximum likelihood estimators, iterative methods must be applied. But this is not easy to implement for the model considered. In this paper, we suggested an alternative method to compute the estimates of the regression parameters and knots. It is shown that the estimates obtained by this method are asymptotically equivalent to the maximum likelihood estimates considered by Chan.     

Nonparametric maximum likelihood estimators for ar and ma time series

The problem of estimating the parameters of moving average or autoregressive time series is studied when the error distribution is completely unknown. Four nonparametric maximum likelihood estimators (NPMLE) are presented for this purpose. These estimators are compared with the classical moment and least squares estimators in a simulation study. The behavior of these NPMLEs is much better than the classical ones, suggesting that they should be used extensively when no parametric information is known in advance about the error distribution. An application of these estimators to coal mining accidents data is also included.     

异方差模型参数估计的有效性研究

本文运用随机模拟方法,对误差序列异方差模型中加权最小二乘（GLS）估计的有效性进行研究。研究表明,GLS估计的有效性与异方差强度有关,当异方差强度较强时,GLS估计比普通最小二乘（OLS）估计有效;当异方差强度较弱时,GLS估计不如OLS估计有效。     

Extended binomial AR(1) processes with generalized binomial thinning operator

Abstract

In this article, we introduce an extended binomial AR(1) model based on the generalized binomial thinning operator. This operator relaxes the independence assumption of the binomial thinning operator and contains dependent Bernoulli counting series. The new model contains the binomial AR(1) model as a particular case. Some probabilistic and statistical properties are explored. Estimators of the model parameters are derived by conditional maximum likelihood (CML), conditional least squares (CLS) and weighted conditional least squares (WCLS) methods. Some asymptotic properties and numerical results of the estimators are studied. The good performance of the new model is illustrated, among other competitive models in the literature, by an application to the monthly drunken driving counts.     

随机效应空间滞后单指数面板模型

对随机效应空间滞后单指数面板模型,本文构建了该模型的截面极大似然估计方法,从理论证明和数值模拟两方面分别考察了其估计量的大样本性质和小样本表现。研究结果表明:(1)在大样本条件下,估计量均具有一致性,并且参数估计量具有渐近正态性。(2)在小样本条件下,各估计量依然具有良好的表现,其精度随着样本容量的增加而提高;空间权重矩阵结构的复杂性对空间相关系数的估计量影响较大,但对其他估计量的影响较小。     

Estimating the error variance in nonparametric regression by a covariate-matched u-statistic

For nonparametric regression models with fixed and random design, two classes of estimators for the error variance have been introduced: second sample moments based on residuals from a nonparametric fit, and difference-based estimators. The former are asymptotically optimal but require estimating the regression function; the latter are simple but have larger asymptotic variance. For nonparametric regression models with random covariates, we introduce a class of estimators for the error variance that are related to difference-based estimators: covariate-matched U-statistics. We give conditions on the random weights involved that lead to asymptotically optimal estimators of the error variance. Our explicit construction of the weights uses a kernel estimator for the covariate density.     

Edgeworth Expansion and Bootstrap Approximation for Studentized Product-Limit Estimator with Truncated and Censored Data

The Yule-Walker estimators of the AR coefficients of a causal multidimensional AR model are obtained by replacing the autocovariances with their estimators in the Yule-Walker equations. It is shown that only unbiased-type estimators of the autocovariances yield consistency of the Yule-Walker estimators. Also, the asymptotic joint distribution of the Yule-Walker estimators is presented.     

Finite sample properties of ml and reml estimators in time series regression models with long memory noise

Finite sample properties of ML and REML estimators in time series regression models with fractional ARIMA noise are examined. In particular, theoretical approximations for bias of ML and REML estimators of the noise parameters are developed and their accuracy is assessed through simulations. The impact of noise parameter estimation on performance of t -statistics and likelihood ratio statistics for testing regression parameters is also investigated.     

Estimation of the mean of the exponential distribution using moving extremes ranked set sampling

Moving Extremes Ranked Set Sampling (MERSS) is a useful modification of Ranked Set Sampling (RSS). Unlike RSS, MERSS allows for an increase of set size without introducing too much ranking error. The method is considered parametrically under exponential distribution. Maximum likelihood estimator (MLE), and a modified MLE are considered and their properties are studied. The method is studied under both perfect and imperfect ranking (with error in ranking). It appears that these estimators can be real competitors to the MLE using the usual simple random sampling (SRS).     

Time series models with asymmetric innovations

We consider AR(q) models in time series with asymmetric innovations represented by two families ofdistributions: (i) gamma with support IR : (0, ∞), and (ii) generalized logistic with support IR:(-∞,∞). Since the ML (maximum likelihood) estimators are intractable, we derive the MML (modified maximum likelihood) estimators of the parameters and show that they are remarkably efficient besides being easy to compute. We investigate the efficiency properties of the classical LS (least squares) estimators. Their efficiencies relative to the proposed MML estimators are very low.     

A comparison of estimators for the mean in the inverse gaussian distribution with a known coefficient of variation

In this paper, we discuss an estimation problem of the mean in the inverse Gaussian distribution with a known coefficient of variation. Two types of linear estimators for the mean, the linear minimum variance unbiased estimator and the linear minimum mean squared error estimator, are constructed by using the squared error loss function and their properties are examined. It is observed that, for small samples the performance of the proposed estimators is better than that of the maximum likelihood estimator, when the coefficient of variation is large.     

Asymptotic normality of Huber–Dutter estimators in a linear model with AR(1) processes

The paper studies a linear regression model with first order autoregressive (AR(1)) processes. The Huber–Dutter (HD) estimators of unknown parameters are given, and the asymptotic normality of the HD estimators is investigated. An example is presented to illustrate the proposed method.     

Estimation of the inverse of mean

For the inverse of mean, a class of estimators with finite moments is considered and its properties are analyzed in the context of normal and non-normal populations.     

Maximum likelihood estimators in regression models with infinite variance innovations

In this paper we consider the problem of maximum likelihood (ML) estimation in the classical AR(1) model with i.i.d. symmetric stable innovations with known characteristic exponent and unknown scale parameter. We present an approach that allows us to investigate the properties of ML estimators without making use of numerical procedures. Finally, we introduce a generalization to the multivariate case.     

On Prediction for Correlated Domains in Longitudinal Surveys

In the survey sampling estimation or prediction of both population’s and subopulation’s (domain’s) characteristics is one of the key issues. In the case of the estimation or prediction of domain’s characteristics one of the problems is looking for additional sources of information that can be used to increase the accuracy of estimators or predictors. One of these sources may be spatial and temporal autocorrelation. Due to the mean squared error (MSE) estimation, the standard assumption is that random variables are independent for population elements from different domains. If the assumption is taken into account, spatial correlation may be assumed only inside domains. In the paper, we assume some special case of the linear mixed model with two random components that obey assumptions of the first-order spatial autoregressive model SAR(1) (but inside groups of domains instead of domains) and first-order temporal autoregressive model AR(1). Based on the model, the empirical best linear unbiased predictor will be proposed together with an estimator of its MSE taking the spatial correlation between domains into account.     

Linear trimmed means for the linear regression with AR(1) errors model

For the linear regression with AR(1) errors model, the robust generalized and feasible generalized estimators of Lai et al. (2003) of regression parameters are shown to have the desired property of a robust Gauss Markov theorem. This is done by showing that these two estimators are the best among classes of linear trimmed means. Monte Carlo and data analysis for this technique have been performed.     

Binomial AR(1) processes: moments,cumulants, and estimation

The modelling and analysis of count-data time series are areas of emerging interest with various applications in practice. We consider the particular case of the binomial AR(1) model, which is well suited for describing binomial counts with a first-order autoregressive serial dependence structure. We derive explicit expressions for the joint (central) moments and cumulants up to order 4. Then, we apply these results for expressing moments and asymptotic distribution of the squared difference estimator as an alternative to the sample autocovariance. We also analyse the asymptotic distribution of the conditional least-squares estimators of the parameters of the binomial AR(1) model. The finite-sample performance of these estimators is investigated in a simulation study, and we apply them to real data about computerized workstations.     

A comparison of LS/ML and GMM estimation in a simple AR(1) model

This paper compares least squares (LS)/maximum likelihood (ML) and generalised method of moments (GMM) estimation in a simple. Gaussian autoregressive of order one (AR(1)) model. First, we show that the usual LS/ML estimator is a corner solution to a general minimisation problem that involves two moment conditions, while the new GMM we devise is not. Secondly, we examine asymptotic and finite sample properties of the new GMM estimator in comparison to the usual LS/ML estimator in a simple AR(1) model. For both stable and unstable (unit root) specifications, we show asymptotic equivalence of the distributions of the two estimators. However, in finite samples, the new GMM estimator performs better.     

第三类Tobit模型的半参数估计方法

本文给出第三类Tobit模型的一种新的半参数估计方法。在独立性假设下,利用主方程和选择方程中可观察受限因变量的条件生存函数所满足的关系式,构造第三类Tobit模型参数的一步联立估计量。在已知选择方程中参数一致性估计量的条件下,这种方法也可用于构造主方程模型参数 的两步估计量。本文证明了所提出的一步联立估计量和两步估计量的一致性和渐近正态性。实验模拟表明,我们提出的估计量在有限样本下具有良好表现,且一步联立估计量的有限样本表现优于或接近于Chen（1997）的估计量。