Exact and Approximate Statistical Inference for Nonlinear Regression and the Estimating Equation Approach

The exact density distribution of the non‐linear least squares estimator in the one‐parameter regression model is derived in closed form and expressed through the cumulative distribution function of the standard normal variable. Several proposals to generalize this result are discussed. The exact density is extended to the estimating equation (EE) approach and the non‐linear regression with an arbitrary number of linear parameters and one intrinsically non‐linear parameter. For a very special non‐linear regression model, the derived density coincides with the distribution of the ratio of two normally distributed random variables previously obtained by Fieler almost a century ago, unlike other approximations previously suggested by other authors. Approximations to the density of the EE estimators are discussed in the multivariate case. Numerical complications associated with the non‐linear least squares are illustrated, such as non‐existence and/or multiple solutions, as major factors contributing to poor density approximation. The non‐linear Markov–Gauss theorem is formulated on the basis of the near exact EE density approximation.     

部分响应形成滤波器的设计

讨论了有最小符号间干扰(ISI)的第一类部分响应滤波器的最佳设计方法。所设计滤波器的选择性和阻带衰减可预先给定并易于控制。以小的频带损失在Nyquist频率附近引入滚降,可使ISI进一步减小。利用这种滤波器还可以获得第四类部分响应信号。给出的设计实例说明这种设计方法很有实用价值。     

寻找非线性演化方程精确解的新的双曲函数法

基于齐次平衡法的思想,利用双曲函数建立了一种求解非线性偏微分方程的新的双曲函数法,其基本原理为,通过作一些特殊的变换,将非线性偏微分方程的求解问题转化为非线性超定代数方程组的求解问题,借助数学软件Mathematica,利用吴消元法等,求解此非线性超定代数方程组,最终获得非线性偏微分方程的精确孤波解.     

对双自由边界Stefan问题的进一步讨论

本文讨论了双自由边界 Stefan 问题的解对于初始条件的单调相依性,以及该解和一个Volterra 型的非线性积分方程组的等价关系。本文所得结果,是对 R.Canno,D.Hill 及 A.Friedman 相应结果的推广。     

MULTIPERIOD FORECASTING ANALYSIS OF A DYNAMIC MODEL FOR A SMALL SAMPLE

In this paper we derive the formulae for the bias and mean squared forecast error (MSFE) of the least squares forecast several periods ahead in the context of a dynamic model. Since the expressions are in terms of integrals, we have also obtained the numerical value of the bias and MSFE for different values of parameters and different disturbance structures. The results confirm some earlier studies (based on the AR(1) model), for example Lahiri (1975) and Hoque et al. (1988).     

一类半线性偏差分方程解的振动性

本文讨论了一类半线性偏差分方程解的振动性，得到了这类方程解的振动性的一些充分条件。     

"新诗二次革命"论的有效性阐释

为了正确理解“新诗二次革命”的主张,消除对“革命论”的敏感与担心,我们必须认识到:第一,“后革命”时期,“诗界革命”与社会革命、政治革命的辩证关系;第二,不能任由新诗自然进化,中国现代诗学对促进新诗的发展已经而且还将产生巨大影响;第三,根据中国现代文化与新诗发展模式的要求,现代诗学必须以辩证否定的方式才能促成新诗的复兴与繁荣。     

Nonparametric testing for no covariate effects in conditional copulas

In dependence modelling using conditional copulas, one often imposes the working assumption that the covariate influences the conditional copula solely through the marginal distributions. This so-called (pairwise) simplifying assumption is almost standardly made in vine copula constructions. However, in recent literature evidence was provided that such an assumption might not be justified. Among the first issues is thus to test for its appropriateness. In this paper nonparametric tests for the null hypothesis of the simplifying assumption are proposed, and their asymptotic behaviours, under the null hypothesis and under some local alternatives, are established. The tests are fully nonparametric in nature: not requiring choices of copula families nor knowledge of the marginals. In a simulation study, the finite-sample size and power performances of the tests are investigated, and compared with these of the few available tests. A real data application illustrates the use of the tests.     

Vague值向Fuzzy值转化的系列方法

提出Vague值向Fuzzy值转化的系列均值法和偏值法．证明了这些方法均满足Vague值向Fuzzy值的转化准     

破解绘画色彩选择的两个障碍

在色彩写生中，能够引起人们审美愉悦、满足人们生理、心理需求的真实绘画色彩的道路上存在着许多障碍，其中“固有色观念”和“局部观察习惯”是经常碰到的易犯病。