Nonparametric Instrumental Regression

The focus of this paper is the nonparametric estimation of an instrumental regression function ϕ defined by conditional moment restrictions that stem from a structural econometric model E[Y−ϕ(Z)|W]=0, and involve endogenous variables Y and Z and instruments W. The function ϕ is the solution of an ill‐posed inverse problem and we propose an estimation procedure based on Tikhonov regularization. The paper analyzes identification and overidentification of this model, and presents asymptotic properties of the estimated nonparametric instrumental regression function.     

一阶非线性常微分方程可积类型的推广

文中提出新的四类非线性常微分方程,借助某些方法与技巧,论证了这几类方程可用积分法求解,获得的结论推广了文献中相应的结果。     

The S-system computation of non-central gamma distribution

The non-central gamma distribution can be regarded as a general form of non-central χ² distributions whose computations were thoroughly investigated (Ruben, H., 1974, Non-central chi-square and gamma revisited. Communications in Statistics, 3(7), 607–633; Knüsel, L., 1986, Computation of the chi-square and Poisson distribution. SIAM Journal on Scientific and Statistical Computing, 7, 1022–1036; Voit, E.O. and Rust, P.F., 1987, Noncentral chi-square distributions computed by S-system differential equations. Proceedings of the Statistical Computing Section, ASA, pp. 118–121; Rust, P.F. and Voit, E.O., 1990, Statistical densities, cumulatives, quantiles, and power obtained by S-systems differential equations. Journal of the American Statistical Association, 85, 572–578; Chattamvelli, R., 1994, Another derivation of two algorithms for the noncentral χ² and F distributions. Journal of Statistical Computation and Simulation, 49, 207–214; Johnson, N.J., Kotz, S. and Balakrishnan, N., 1995, Continuous Univariate Distributions, Vol. 2 (2nd edn) (New York: Wiley). Both distributional function forms are usually in terms of weighted infinite series of the central one. The ad hoc approximations to cumulative probabilities of non-central gamma were extended or discussed by Chattamvelli, Knüsel and Bablok (Knüsel, L. and Bablok, B., 1996, Computation of the noncentral gamma distribution. SIAM Journal on Scientific Computing, 17, 1224–1231), and Ruben (Ruben, H., 1974, Non-central chi-square and gamma revisited. Communications in Statistics, 3(7), 607–633). However, they did not implement and demonstrate proposed numerical procedures. Approximations to non-central densities and quantiles are not available. In addition, its S-system formulation has not been derived. Here, approximations to cumulative probabilities, density, and quantiles based on the method of Knüsel and Bablok are derived and implemented in R codes. Furthermore, two alternate S-system forms are recast on the basis of techniques of Savageau and Voit (Savageau, M.A. and Voit, E.O., 1987, Recasting nonlinear differential equations as S-systems: A canonical nonlinear form. Mathematical Biosciences, 87, 83–115) as well as Chen (Chen, Z.-Y., 2003, Computing the distribution of the squared sample multiple correlation coefficient with S-Systems. Communications in Statistics—Simulation and Computation, 32(3), 873–898.) and Chen and Chou (Chen, Z.-Y. and Chou, Y.-C., 2000, Computing the noncentral beta distribution with S-system. Computational Statistics and Data Analysis, 33, 343–360.). Statistical densities, cumulative probabilities, quantiles can be evaluated by only one numerical solver power low analysis and simulation (PLAS). With the newly derived S-systems of non-central gamma, the specialized non-central χ² distributions are demonstrated under five cases in the same three situations studied by Rust and Voit. Both numerical values in pairs are almost equal. Based on these, nine cases in three similar situations are designed for demonstration and evaluation. In addition, exact values in finite significant digits are provided for comparison. Demonstrations are conducted by R package and PLAS solver in the same PC system. By doing these, very accurate and consistent numerical results are obtained by three methods in two groups. On the other hand, these three methods are performed competitively with respect to speed of computation. Numerical advantages of S-systems over the ad hoc approximation and related properties are also discussed.     

Robustness to non-normality and autocorrelation of individuals control charts

This paper studies the effects of non-normality and autocorrelation on the performances of various individuals control charts for monitoring the process mean and/or variance. The traditional Shewhart X chart and moving range (MR) chart are investigated as well as several types of exponentially weighted moving average (EWMA) charts and combinations of control charts involving these EWMA charts. It is shown that the combination of the X and MR charts will not detect small and moderate parameter shifts as fast as combinations involving the EWMA charts, and that the performana of the X and MR charts is very sensitive to the normality assumption. It is also shown that certain combinations of EWMA charts can be designed to be robust to non-normality and very effective at detecting small and moderate shifts in the process mean and/or variance. Although autocorrelation can have a significant effect on the in-control performances of these combinations of EWMA charts, their relative out-of-control performances under independence are generally maintained for low to moderate levels of autocorrelation.     

Accurate ARL computation for EWMA-S<Superscript>2</Superscript> control charts

Originally, the exponentially weighted moving average (EWMA) control chart was developed for detecting changes in the process mean. The average run length (ARL) became the most popular performance measure for schemes with this objective. When monitoring the mean of independent and normally distributed observations the ARL can be determined with high precision. Nowadays, EWMA control charts are also used for monitoring the variance. Charts based on the sample variance S² are an appropriate choice. The usage of ARL evaluation techniques known from mean monitoring charts, however, is difficult. The most accurate method—solving a Fredholm integral equation with the Nyström method—fails due to an improper kernel in the case of chi-squared distributions. Here, we exploit the collocation method and the product Nyström method. These methods are compared to Markov chain based approaches. We see that collocation leads to higher accuracy than currently established methods.     

一类混合指数型算子的一致逼近

主要讨论了一类混合指数型算子的一致逼近问题，并给出了逼近阶的估计和特征刻划。     

一个半离散的Hilbert型不等式及其等价形式

应用权系数方法给出的一个新的带有最佳常数的一个半离散的Hilbert不等式,同时出给相应的等价形式.     

具有高次积分的二阶三阶常微分方程的结构定理

本文利用确定高次积分因子的引理与确定对应的高次积分的公式以及微分特征列集(吴)方法,给出了拥有高次积分的二阶三阶常微分方程结构定理.     

原始悲剧:中国古典悲剧的理论界定

本文从中国古典悲剧形态的“喜剧性”情结人手,通过一种广泛的文化比较研究,从民俗学的角度探讨中国古典悲剧与“季节神话”的神话学渊源;从哲学的角度探讨中国古典悲剧与儒、道思想的认识论关系;从美学的角度探讨中国古典悲剧与尼采悲剧观的“同质”现象;从人类学的角度探讨中国古典悲剧的存在意义;从而得出中国古典悲剧其实是一种原始悲剧的结论,进而指出中国古典悲剧与黑格尔“古典悲剧”的“异质”之处.     

英语课文整体教学法的优势

英语课文整体教学在教学中具有明显的优势有利于教学观念更新;有利于培养能力;有利于优化课堂结构;有利于教学手段现代化。