分位数回归及应用简介

文章介绍了分位数回归法的概念、算法及主流统计软件R和SAS计算时的语法,并通过实例与以普通最小二乘法为基础的线性回归进行了对比,展现了分位数回归的巨大魅力。     

Semiparametric linear transformation models for current status data

Current status data arise when the death of every subject in a study cannot be determined precisely, but is known only to have occurred before or after a random monitoring time. The authors discuss the analysis of such data under semiparametric linear transformation models for which they propose a general inference procedure based on estimating functions. They determine the properties of the estimates they propose for the regression parameters of the model and illustrate their technique using tumorigenicity data.     

Joint impact of multiple observations on a subset of variables in multiple linear regression

In multiple linear regression analysis, each observation affects the fitted regression equation differently and has varying influences on the regression coefficients of the different variables. Chatterjee & Hadi (1988) have proposed some measures such as DSSE_ij (Impact on Residual Sum of Squares of simultaneously omitting the ith observation and the jth variable), F_j (Partial F-test for the jth variable) and F_j(i) (Partial F-test for the jth variable omitting the ith observation) to show the joint impact and the interrelationship that exists among a variable and an observation. In this paper we have proposed more extended form of those measures DSSE_IJ, F_J and F_J(I) to deal with the interrelationships that exist among the multiple observations and a subset of variables by monitoring the effects of the simultaneous omission of multiple variables and multiple observations.     

Implementing partial least squares

Partial least squares (PLS) regression has been proposed as an alternative regression technique to more traditional approaches such as principal components regression and ridge regression. A number of algorithms have appeared in the literature which have been shown to be equivalent. Someone wishing to implement PLS regression in a programming language or within a statistical package must choose which algorithm to use. We investigate the implementation of univariate PLS algorithms within FORTRAN and the Matlab (1993) and Splus (1992) environments, comparing theoretical measures of execution speed based on flop counts with their observed execution times. We also comment on the ease with which the algorithms may be implemented in the different environments. Finally, we investigate the merits of using the orthogonal invariance of PLS regression to improve the algorithms.     

小麦新品种“绵阳26”主要性状与产量的关系

对45个试验点的资料分析,多抗、丰产、优质、广适小麦新品种绵阳26的主要性状有效穗x1、穗粒数x2和千粒x3、单穗重x4与产量y的回归方程为：y＝－614．8425＋9.8683x1＋7.3223x2＋10．5315x3＋22．5748x4。经偏回归和偏相关分析,产量构成因素中,千粒重、有效穗对绵阳26产量的贡献和影响最大（b'3＝1．7435,b'1＝1．5372,R3y.＝0．7983,R1y＝0．6991）。在现有产量的基础上稳定千粒重,主攻穗数和穗粒数,是发挥绵阳26高产潜力的决定因素。     

Spatial variation in risk of disease: a nonparametric binary regression approach

A common problem in environmental epidemiology is the estimation and mapping of spatial variation in disease risk. In this paper we analyse data from the Walsall District Health Authority, UK, concerning the spatial distributions of cancer cases compared with controls sampled from the population register. We formulate the risk estimation problem as a nonparametric binary regression problem and consider two different methods of estimation. The first uses a standard kernel method with a cross-validation criterion for choosing the associated bandwidth parameter. The second uses the framework of the generalized additive model (GAM) which has the advantage that it can allow for additional explanatory variables, but is computationally more demanding. For the Walsall data, we obtain similar results using either the kernel method with controls stratified by age and sex to match the age–sex distribution of the cases or the GAM method with random controls but incorporating age and sex as additional explanatory variables. For cancers of the lung or stomach, the analysis shows highly statistically significant spatial variation in risk. For the less common cancers of the pancreas, the spatial variation in risk is not statistically significant.     

Application of Markov chain Monte Carlo methods to modelling birth prevalence of Down syndrome

Data collected before the routine application of prenatal screening are of unique value in estimating the natural live-birth prevalence of Down syndrome. However, much of these data are from births from over 20 years ago and they are of uncertain quality. In particular, they are subject to varying degrees of underascertainment. Published approaches have used ad hoc corrections to deal with this problem or have been restricted to data sets in which ascertainment is assumed to be complete. In this paper we adopt a Bayesian approach to modelling ascertainment and live-birth prevalence. We consider three prior specifications concerning ascertainment and compare predicted maternal-age-specific prevalence under these three different prior specifications. The computations are carried out by using Markov chain Monte Carlo methods in which model parameters and missing data are sampled.     

上海股票市场股票收益率因素研究

根据上海股票市场从1995 年7 月到2000 年6 月所有A 股股票的月收益率、价格、市值和 公司财务数据,利用Fama-Macbeth 回归分析方法及构造动态组合方法,分析总市值、流通市值、 价格、账面市值比、市盈率、账面资产负债比等因素对股票回报率的影响. 发现上海股票市场具 有显著的市值效应、账面市值比效应、市盈率效应和价格效应. 这些效应不能用股票的beta 值 来解释. 同时发现Fama- French 的三因子模型不能完全解释这些效应,但在三因子模型的基础 上再加上一个市盈率因子可以很好地解     

基于GRPLS 回归的 中国经济增长影响因素分析

构造一种新的方法———岭- 偏最小二乘回归方法(它既有效消除了因素变量之间的多 重共线性,又克服了传统方法的不足,且使模型更加稳健,具有更强的预测和分析能力) ;并运 用广义岭- 偏最小二乘回归方法分析了我国经济增长的影响因素,为我国制订持续、快速增长 的经济政策提供了有益的参考.     

动力减振器最优参数的非线性回归和若干问题

本文采用最优化方法求得考虑生系统阻尼的动力减振器最优参数集，并对此参数集进行非线性回归，得到了便于动力减振器最优设计的回归曲线族。本文还对现有的主系统无阻尼时动力减振器最优参数公式进行了讨论，指出了这些公式的局限性，并根据本文的结果给出了应用范围更广泛的改进公式。