On the Rounded Integer-Valued Autoregressive Process

In recent years, there has been a growing interest in modelling integred-valued time series. In this article, we propose a modified and generalized version of the first order rounded integer-valued autoregressive RINAR(1) model, originally introduced by Kachour and Yao (2009 Kachour , M. , Yao , J. F. ( 2009 ). First-order rounded integer-valued autoregressive (RINAR(1)) process . Journal of Time Series Analysis 30 ( 4 ): 417 – 448 .[Crossref], [Web of Science ®] , [Google Scholar]). Indeed, this class can be considered as an alternative of classical models based on the thinning operators. Using a Markov chain method, conditions for stationarity and the existence of moments are investigated. Least squares estimator of the model parameters is considered and its consistence is established. Finally, we describe the price change data using a model of the new class.     

Statistical Analysis of Parameter Estimation for 2-D Harmonics in Multiplicative and Additive Noise

This article considers the problem of parameter estimation for two dimensional (2-D) multi-component harmonics in non zero-mean multiplicative and additive noise. The least squares estimators (LSEs) are proposed to estimate the coherent model parameters, and some statistical results of the LSEs are obtained, including strong consistency, strong convergence rate, and asymptotic normality. Furthermore, the LSEs-based estimators are proposed to estimate the noncoherent model parameters, and the strong consistency and the asymptotic normality are also proved. Finally, some numerical experiments are performed to see how the asymptotic results work for finite sample sizes.     

A note on properties of spatial yule-walker estimators

For two-dimensional spatial autoregressive (AR) models, asymptotic properties of the spatial Yule-Walker (YW) estimators (Tjøstheim, 1978) are studied. These estimators although consistent, are shown to be asymptotically biased. Estimators from the first-order spatial bilateral AR model are looked at in more detail and the spatial YW estimators for this model are compared with the exact maximum likelihood estimators. Small sample properties of both estimators are also discussed briefly and some simulation results are presented.     

An efficient and fast algorithm for estimating the parameters of two-dimensional sinusoidal signals

In this paper we propose a computationally efficient algorithm to estimate the parameters of a 2-D sinusoidal model in the presence of stationary noise. The estimators obtained by the proposed algorithm are consistent and asymptotically equivalent to the least squares estimators. Monte Carlo simulations are performed for different sample sizes and it is observed that the performances of the proposed method are quite satisfactory and they are equivalent to the least squares estimators. The main advantage of the proposed method is that the estimators can be obtained using only finite number of iterations. In fact it is shown that starting from the average of periodogram estimators, the proposed algorithm converges in three steps only. One synthesized texture data and one original texture data have been analyzed using the proposed algorithm for illustrative purpose.     

Least Squares Consistent Estimates for Arbitrary Regression Functions Over an Abstract Space

In this article, we propose a new approach to sieve estimation for a general regression function when the dimension of the finite dimensional subspaces is a random quantity depending on the values of the observations.

The technique is introduced with the help of a simulation study on a functional linear model under extremely mild assumptions.

A sketch of the proof concerning the main statements is then given in the more general case when the regression function is not necessarily linear.     

On the correct regression function (in L2) and its applications when the dimension of the covariate vector is random

We derive the optimal regression function (i.e., the best approximation in the L₂ sense) when the vector of covariates has a random dimension. Furthermore, we consider applications of these results to problems in statistical regression and classification with missing covariates. It will be seen, perhaps surprisingly, that the correct regression function for the case with missing covariates can sometimes perform better than the usual regression function corresponding to the case with no missing covariates. This is because even if some of the covariates are missing, an indicator random variable δ$\delta$, which is always observable, and is equal to 1 if there are no missing values (and 0 otherwise), may have far more information and predictive power about the response variable Y than the missing covariates do. We also propose kernel-based procedures for estimating the correct regression function nonparametrically. As an alternative estimation procedure, we also consider the least-squares method.     

Estimation of parameters in heavy-tailed distribution when its second order tail parameter is known

Estimating parameters in heavy-tailed distribution plays a central role in extreme value theory. It is well known that classical estimators based on the first order asymptotics such as the Hill, rank-based and QQ estimators are seriously biased under finer second order regular variation framework. To reduce the bias, many authors proposed the so-called second order reduced bias estimators for both first and second order tail parameters. In this work, estimation of parameters in heavy-tailed distributions are studied under the second order regular variation framework when the second order parameter in the distribution tail is known. This is motivated in large part by a recent work by the authors showing that the second order tail parameter is known for a large class of popular random difference equations (for example, ARCH models). The focus is on least squares estimators that generalize rank-based and QQ estimators. Though other possible estimators are also briefly discussed, the least squares estimators are most simple to use and perform best for finite samples in Monte Carlo simulations.     

简论李觏的土地思想

李觏是北宋中期重要的思想家,在李觏的整个思想体系中,经济思想占有很重要的地位。李觏非常重视土地问题,土地思想是李觏经济思想的核心。针对当时土地兼并日益激烈引起的社会危害,李觏也提出了关于土地问题的看法。他的土地思想经历了前后两个时期,前期主要从分配角度分析,主张平土均田。后期主要从生产角度批判土地兼并。李觏提出了＂平土均田＂、＂井田制＂、＂农业劳动力＂、＂尽地力、广垦辟＂、＂限田＂等抑制土地兼并,发展农业,保护农民利益的思想。     

On the accuracy and cost of numerical integration in several variables ∗

Identical numerical integration experiments are performed on a CYBER 205 and an IBM 3081 in order to gauge the relative performance of several methods of integration. The methods employed are the general methods of Gauss-Legendre, iterated Gauss-Legendre, Newton-Cotes, Romberg and Monte Carlo as well as three methods, due to Owen, Dutt, and Clark respectively, for integrating the normal density. The bi- and trivariate normal densities and four other functions are integrated; the latter four have integrals expressible in closed form and some of them can be parameterized to exhibit singularities or highly periodic behavior. The various Gauss-Legendre methods tend to be most accurate (when applied to the normal density they are even more accurate than the special purpose methods designed for the normal) and while they are not the fastest, they are at least competitive. In scalar mode the CYBER is about 2-6 times faster than the IBM 3081 and the speed advantage of vectorised to scalar mode ranges from 6 to 15. Large scale econometric problems of the probit type should now be routinely soluble.