递归均值调整单位根检验能提高检验功效吗?

根据备择假设成立时均值是否为零,讨论了三类单位根检验统计量的检验功效。理论研究表明:在大样本下,检验功效只与检验类型有关,与均值取值无关。蒙特卡洛模拟表明:在有限样本下,均值会影响检验功效,当均值为零时,第一类DF检验功效最高;当均值大于零时,在绝大多数场合下,第二类DF检验功效最优。因此,递归均值调整单位根检验功效仅在有限条件下最大。     

Consistency of the recursive nonparametric regression estimation for dependent functional data

We consider the recursive estimation of a regression functional where the explanatory variables take values in some functional space. We prove the almost sure convergence of such estimates for dependent functional data. Also we derive the mean quadratic error of the considered class of estimators. Our results are established with rates and asymptotic appear bounds, under strong mixing condition. Finally, the feasibility of the proposed estimator is illustrated throughout an empirical study.     

A statistical analysis of the screening measure of multiple recursive random number generators of orders one and two

This paper presents the results of a comprehensive empirical analysis of the screening measure of multiple recursive generators (MRGs) of orders one and two. Two kinds of screening measures are distinguished: spectral test and lattice test. With regard to these screening measures, two exhaustive searches of the twenty best MRGs of orders one and two are conducted. Some empirical comparisons reveal that the screening procedure with maximum spectral value criterion is preferred in terms of efficiency and thus, is a good way of obtaining ideal MRGs of higher orders. Several extensively tested second-order MRGs are also presented and are therefore recommended.     

悖论的语言结构:递归否定

悖论是逻辑学、基础数学、哲学、语言学中的重要问题,从根本上看是一个认识论问题,因此仅仅从人工语言的角度来认识悖论是不充分的,因为人工语言不能解决元语言这一根本问题。自然语言是最根本的元语言,悖论更需要从自然语言的角度来认识,尤其是从自然语言结构的递归性来认识。通常把悖论分成逻辑悖论(集合悖论)和语义悖论两大类,但这种分类界限并不严格。实际上这两类悖论从语言生成的角度看都具有递归否定的特点,因此可以用递归否定这一语言结构性质来统一语法悖论和语义悖论。罗素的类型论和塔尔斯基语义理论主要涉及产生悖论的层阶性质,不能概括悖论的递归否定性质。自然语言和形式语言都是从有限规则和有限符号到无限句子的系统,不可能避免层阶循环或递归,因此悖论的消除不可能通过类型论或元语言层阶来解决,考虑递归否定的性质是消除悖论的一个途径。     

程序设计中的递归算法教学探讨

递归算法是程序设计中的常用算法之一 ,也是一种重要的编程方法。掌握递归方法十分重要 ,但递归算法是较难理解和掌握的。因此 ,有必要对如何讲好递归算法做一些探讨。分析了递归算法的特点 ,指出了在递归教学中存在的一些问题 ,并给出了一种有效的解决方法     

一类组合计数问题

考察了满足一定限制条件的长度为ｎ具有ｍ个水平的数列计数问题，给出了它们的递归式和显表达式；改进了钥匙编码组合计数中的一个结果并得到几个组合恒等式     

A kind of stochastic recursive Zero-Sum differential game problem with double obstacles constraint

Abstract

This paper concerns a class of stochastic recursive zero-sum differential game problem with recursive utility related to a backward stochastic differential equation (BSDE) with double obstacles. A sufficient condition is provided to obtain the saddle-point strategy under some assumptions. In virtue of the corresponding relationship of doubly reflected BSDE and mixed game problem, a stochastic linear recursive mixed differential game problem is studied to apply our theoretical result, and here the explicit saddle-point strategy as well as the saddle-point stopping time for the mixed game problem are obtained. Besides, a numeral example is also given to demonstrate the result by virtue of partial differential equations (PDEs) computation method.     

Some notes on Church's thesis and the theory of games

This paper considers games in normal form played by Turing Machines. The machines are fed as input all the relevent information and then are required to play the game. Some impossibility results are derived for this set-up. In particular, it is shown that no Turing Machine exists which will always play the correct strategy given its opponent's choice. Such a result also generalizes to the case in which attention is restricted to economically optimizing machines only. The paper also develops a model of knowledge. This allows the main results of the paper to be interpreted as stemming out of the impossibility of always deciding whether a player is rational or not in some appropriate sense.     

On the power of some tests for examining the stability of regression coefficients

The main objective of the study is to compare four different procedures to test for the stability of regression coefficients. The comparisons are based on a numerical study and are with respect to their abilities to detect various simple forms of parameter instabilities. Besides the power comparisons a special interest is directed towards the choice of “window length” in the tests based on moving sums of squared recursive and ordinary least-squares residuals.     

一种广义预测状态空间递推算法

本文从广义预测控制（ＧＰＣ） 基本算法原理出发,给出了一种广义预测状态空间描述,从而使得确定预测控制律的大部分信息可以由状态方程递推获得,使ＧＰＣ 算法的计算量大大减少．