An alternative derivation of the Kalman filter using the quasi-likelihood method

The Kalman filter gives a recursive procedure for estimating state vectors. The recursive procedure is determined by a matrix, so-called gain matrix, where the gain matrix is varied based on the system to which the Kalman filter is applied. Traditionally the gain matrix is derived through the maximum likelihood approach when the probability structure of underlying system is known. As an alternative approach, the quasi-likelihood method is considered in this paper. This method is used to derive the gain matrix without the full knowledge of the probability structure of the underlying system. Two models are considered in this paper, the simple state space model and the model with correlated between measurement and transition equation disturbances. The purposes of this paper are (i) to show a simple way to derive the gain matrix; (ii) to give an alternative approach for obtaining optimal estimation of state vector when underlying system is relatively complex.     

Semiparametric Regression with Kernel Error Model

Abstract.  We propose and study a class of regression models, in which the mean function is specified parametrically as in the existing regression methods, but the residual distribution is modelled non-parametrically by a kernel estimator, without imposing any assumption on its distribution. This specification is different from the existing semiparametric regression models. The asymptotic properties of such likelihood and the maximum likelihood estimate (MLE) under this semiparametric model are studied. We show that under some regularity conditions, the MLE under this model is consistent (when compared with the possibly pseudo-consistency of the parameter estimation under the existing parametric regression model), is asymptotically normal with rate and efficient. The non-parametric pseudo-likelihood ratio has the Wilks property as the true likelihood ratio does. Simulated examples are presented to evaluate the accuracy of the proposed semiparametric MLE method.     

会计估计审计之探讨

本文着重探讨了审计工作过程中遇到的越来越多的会计估计审计问题,重点阐述了会计估计事项真实性、金额的准确性和变更合理性的审计难度,并提出了针对上述问题的工作方法。     

Estimating a Convex Function in Nonparametric Regression

Abstract.  A new nonparametric estimate of a convex regression function is proposed and its stochastic properties are studied. The method starts with an unconstrained estimate of the derivative of the regression function, which is firstly isotonized and then integrated. We prove asymptotic normality of the new estimate and show that it is first order asymptotically equivalent to the initial unconstrained estimate if the regression function is in fact convex. If convexity is not present, the method estimates a convex function whose derivative has the same L ^p -norm as the derivative of the (non-convex) underlying regression function. The finite sample properties of the new estimate are investigated by means of a simulation study and it is compared with a least squares approach of convex estimation. The application of the new method is demonstrated in two data examples.     

Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm

Two new implementations of the EM algorithm are proposed for maximum likelihood fitting of generalized linear mixed models. Both methods use random (independent and identically distributed) sampling to construct Monte Carlo approximations at the E-step. One approach involves generating random samples from the exact conditional distribution of the random effects (given the data) by rejection sampling, using the marginal distribution as a candidate. The second method uses a multivariate t importance sampling approximation. In many applications the two methods are complementary. Rejection sampling is more efficient when sample sizes are small, whereas importance sampling is better with larger sample sizes. Monte Carlo approximation using random samples allows the Monte Carlo error at each iteration to be assessed by using standard central limit theory combined with Taylor series methods. Specifically, we construct a sandwich variance estimate for the maximizer at each approximate E-step. This suggests a rule for automatically increasing the Monte Carlo sample size after iterations in which the true EM step is swamped by Monte Carlo error. In contrast, techniques for assessing Monte Carlo error have not been developed for use with alternative implementations of Monte Carlo EM algorithms utilizing Markov chain Monte Carlo E-step approximations. Three different data sets, including the infamous salamander data of McCullagh and Nelder, are used to illustrate the techniques and to compare them with the alternatives. The results show that the methods proposed can be considerably more efficient than those based on Markov chain Monte Carlo algorithms. However, the methods proposed may break down when the intractable integrals in the likelihood function are of high dimension.     

中国国有经济规模与经济增长条件收敛——基于1978—2008年省际面板数据的实证研究

文章揭示了中国国有经济规模对区域经济增长条件收敛的影响。在研究过程中,文章扩展了Mankiw、Romer和Weil(1992)等修正的附加人力资本的新古典增长模型,将国有经济规模等制度性变量纳入其中,使用中国省级面板数据,运用动态面板数据一阶差分GMM估计方法。实证结果显示,在控制了其他影响因素之后,如果用"国有经济单位职工人数占各地区职工总人数的比重"和"国有经济单位固定资产投资占全社会固定资产投资的比重"这两个变量来衡量国有经济规模,那么国有经济规模在全国和东部地区都是经济增长条件收敛的一个影响因素,并对经济增长产生负面影响;在中部,国有经济规模不是经济增长条件收敛的影响因素;在西部,国有经济规模可能是经济增长的一个促进因素,并且影响区域经济增长条件收敛。     

国债的经济效应与李嘉图等价——基于战后日本数据的实证检验

关于国债经济效应的理论研究中,李嘉图等价定理处于核心地位并产生了深远的影响。如果李嘉图等价定理成立,那么通过发行国债所实施的积极财政政策将是无效的;反之将是有效的。通过综合运用间接和直接检验对李嘉图等价定理进行实证分析可以验证:国债政策的运用对战后日本经济的发展起到了积极影响。此外,通过对影响日本私人消费的相关因素(家庭可支配收入、政府消费和国债)运用可变参数状态空间模型进行估计,从而分析了各影响因素对消费弹性的动态变化。     

城市化发展与房地产价格的相关性研究

城市化所导致的人口大量迁移引起了对房地产的庞大需求。对未来十年城市化发展所带来的房地产业需求规模进行预测,并使用OLS回归估计进行证明的结果表明,城市化发展水平与高房价二者之间存在显著的相关性。     

Empirical likelihood for generalized linear models with fixed and adaptive designs

Empirical likelihood inference for generalized linear models with fixed and adaptive designs is considered. It is shown that the empirical log-likelihood ratio at the true parameters converges to the standard chi-square distribution. Furthermore, we obtain the maximum empirical likelihood estimate of the unknown parameter and the resulting estimator is shown to be asymptotically normal. Some simulations are conducted to illustrate the proposed method.     

Bayesian analysis for the two-parameter Pareto distribution based on record values and times

Doostparast and Balakrishnan (Pareto record-based analysis, Statistics, under review) recently developed optimal confidence intervals as well as uniformly most powerful tests for one- and two-sided hypotheses concerning shape and scale parameters, for the two-parameter Pareto distribution based on record data. In this paper, on the basis of record values and inter-record times from the two-parameter Pareto distribution, maximum-likelihood and Bayes estimators as well as credible regions are developed for the two parameters of the Pareto distribution. For illustrative purposes, a data set on annual wages of a sample of production-line workers in a large industrial firm is analysed using the proposed procedures.