Abnormal behavior of the least squares estimate of multiple regression

An example is given to reveal the abnormal behavior of the least squares estimate of multiple regression. It is shown that the least squares estimate of the multiple linear regression may be “improved” in the sense of weak consistency when nuisance parameters are introduced into the model. A discussion on the implications of this finding is given.     

对差分光学吸收光谱法的监测数据进行实时预测研究

差分光学吸收光谱法（DOAS）已经成为测量大气中微量气体浓度广泛应用的方法.通过对大气差分吸收光谱的分析可以得到它们的浓度.但在恶劣气候条件下，DOAS系统不能获得连续的实时监测数据，因此不能满足我国环境监测条例对环境监测子站的要求.文中提出了一种利用逐步回归分析的方法，对DOAS系统的监测数据进行实时预测.通过大量的对比实验表明，利用该方法得到的预测结果与实际测量结果一致，目前该技术已经被应用于DOAS监测仪器中. 关键词： 差分光学吸收光谱法（DOAS） 逐步回归分析 预测     

删失场合半参数回归模型的二阶段估计

对于半参数回归模型ｙｉ＝ｘ′ｉβ＋ｇ（ｔｉ）＋ｅｉ，１≤ｉ≤ｎ，ｇ为Ｒ１上未知函数，β为ｐ×１维待估参数向量．本文考虑当ｙｉ被随机删失时β和ｇ的估计．基于模型的可加性，利用综合数据法得到β的二阶段估计β～＊ｎ和ｇ的估计ｇ＊ｎ，并证明了它们的强相合性．     

NA样本密度函数估计一致渐近正态性的收敛速度

在平稳NA样本下,讨论了未知密度函数估计的一致渐近正态性.在适当的条件下给出了该密度函数估计一致渐近正态性的收敛速度.这个速度几乎达到n^{-1/6}     

广义线性回归拟似然估计的强相合性

本文研究了广义线性模型g=μ(x'β0)+e中形如的拟似然方程,在一定的条件下证明了当n充分大时此方程以概率1有解βn,得到了βn的强相合性和收敛速度.     

Regression Modeling of the Acousto-Biomechanical Characteristics of Wheezes during Human Forced Expiration

Within the framework of a specified acousto-biomechanical model, a possibility of explaining wheezes during forced expiration on the basis of a vortex separation mechanism is tested and the localization of the zones in the bronchial tree where forced expiratory wheezes are generated is refined. As an experimental model, a group of 18 healthy volunteers from 18 to 44 years old (median is equal 19) was used. On the basis of linear regression modeling the relationship between the principal spectral frequency of medium-frequency forced expiratory wheezes (400–600 Hz) recorded on the trachea and the standard volume flow-rates of expired air measured in computer spirometry is analyzed. The data obtained show that vortex separation in the air flow at the bronchial tree bifurcations (where a stepwise increase in the cross-section area takes place) is a probable mechanism of medium-frequency forced expiratory wheeze generation and that during the forced expiratory maneuver the vortex separation zone tends to be displaced deeper into the bronchial tree.     

Correlation between the Optical Properties and Structure of GRS-Active Substrates Based on Silver Films

The relationship between the optical properties of GRS-active substrates based on silver films and the parameters of their surface roughness have been studied by methods of mathematical statistics (correlation, regression, and factor analyses). The equations of nonlinear regression connecting these quantities were obtained. It is established that most correlatable are the maximum value of the optical density with the distance between islands and with the coefficient of their shape, and also its relation to the halfwidth of the optical density band of a silver film with the mentioned characteristics of the islands.     

Bayesian estimation of NIG models via Markov chain Monte Carlo methods

The normal inverse Gaussian (NIG) distribution is a promising alternative for modelling financial data since it is a continuous distribution that allows for skewness and fat tails. There is an increasing number of applications of the NIG distribution to financial problems. Due to the complicated nature of its density, estimation procedures are not simple. In this paper we propose Bayesian estimation for the parameters of the NIG distribution via an MCMC scheme based on the Gibbs sampler. Our approach makes use of the data augmentation provided by the mixture representation of the distribution. We also extend the model to allow for modelling heteroscedastic regression situations. Examples with financial and simulated data are provided. Copyright © 2004 John Wiley & Sons, Ltd.     

Multiple regression on stable vectors

We give necessary and sufficient conditions for the linearity of multiple regression on a general stable vector, along with a sufficient condition for the finiteness of the conditional absolute moment when 0 < α ≤ 1.     

带有异方差的部分线性回归模型的B样条估计

考虑一带有异方差的固定设计部分线性回归模型yij=X'ijβ+g(tij)+εij,i=1,2…,k:j=1,2,…,ni,和sum from i=1 to kni=n,其中yij为响应变量,β=(β1,…,βp)’是未知的参数向量,g(·)是未知的函数,Xij=(Xij1,…,Xijp)’和tij∈[0,1]为已知的非随机设计点,εij为均值0,方差是σi2的随机误差,其中σi2可能不同.通过B样条级数近似非参数分量,构造了参数分量β的一个半参数广义最小二乘估计.在一些矩条件下,导出了此半参数广义最小二乘估计的渐近分布,大多数在实际中遇到的误差分布都满足这些矩条件.另外,也构造了半参数广义最小二乘估计的渐近协方差矩阵的一个相合估计,还讨论了非参数分量的B样条估计.所有这些大样本性质都是在k趋于无穷大,ni有限时导出的.这些结果能被用来做渐近有效的统计推导.