Testing heteroscedasticity in nonparametric regression

The importance of being able to detect heteroscedasticity in regression is widely recognized because efficient inference for the regression function requires that heteroscedasticity is taken into account. In this paper a simple consistent test for heteroscedasticity is proposed in a nonparametric regression set-up. The test is based on an estimator for the best L ²-approximation of the variance function by a constant. Under mild assumptions asymptotic normality of the corresponding test statistic is established even under arbitrary fixed alternatives. Confidence intervals are obtained for a corresponding measure of heteroscedasticity. The finite sample performance and robustness of these procedures are investigated in a simulation study and Box-type corrections are suggested for small sample sizes.     

涟水县,锡山市生育率影响因素的调查分析

从统计事实出发,比较锡山市、涟水县两个地区的生育差异、分析造成生育差异的经济社会文化因素,用理论模型来揭示文化和生育的本质联系和文化对生育的影响机制和途径。     

水泥土桩复合地基承载力取值方法探讨

水泥土桩复合地基承载力的确定,目前常用的方法是现场载荷试验,并被公认为是比较可靠的方法。结合工程实测资料,讨论了用该法确定水泥土极复合地基承载力的取值问题,提出用相对变形S认的取值是合理的。同时通过一定数量的水泥土单桩静载荷试验、单极复合地基载荷试验和多桩复合地基载荷试验对比分析,说明用一组极和桩间土所组成的单元作进行承载力试验,更接近实际复合地基的受力性状和承载机理。     

施工质量责任引发损害赔偿问题的思考

在建设工程中由于施工质量原因而侵犯房屋所有人财产、人身权利,并引起一系列与民事损害赔偿相关的法律问题多有出现。但对于民事责任的承担,由于没有一部统一的法律调整双方当事人权利义务,因此在实践处理中存在较大的任意性。结合实践,依据相关的法律、法规、司法解释提出解决有关问题的应适用的法律。     

Local influence in ridge semiparametric models

ABSTRACT

Ridge penalized least-squares estimators has been suggested as an alternative to the minimum penalized sum of squares estimates in the presence of collinearity among the explanatory variables in semiparametric regression models (SPRMs). This paper studies the local influence of minor perturbations on the ridge estimates in the SPRM. The diagnostics under the perturbation of ridge penalized sum of squares, response variable, explanatory variables and ridge parameter are considered. Some local influence diagnostics are given. A Monte Carlo simulation study and a real example are used to illustrate the proposed perturbations.     

生育权利化的法哲学思考

生育权由自然权利向法律权利转化,是由社会基本条件决定的,一方面生育利益的外部冲突是促成转化的外因,另一方面生育利益的内部冲突是促成转化的內因。我国生育立法虽然确认生育是一种权利,但在权利保护方面,仍然存在不足,亟待完善。     

农业生态旅游地可持续发展评价体系研究

农业生态旅游的无序发展违背了可持续原则,构建基于目的承载力农业生态旅游可持续发展模型,兼顾了包括社会经济承载力、资源承载力和环境承载力的承载力指数和人文发展指数,推进农业生态旅游的持续发展。     

On a tobit–Birnbaum–Saunders model with an application to medical data

The tobit model allows a censored response variable to be described by covariates. Its applications cover different areas such as economics, engineering, environment and medicine. A strong assumption of the standard tobit model is that its errors follow a normal distribution. However, not all applications are well modeled by this distribution. Some efforts have relaxed the normality assumption by considering more flexible distributions. Nevertheless, the presence of asymmetry could not be well described by these flexible distributions. A real-world data application of measles vaccine in Haiti is explored, which confirms this asymmetry. We propose a tobit model with errors following a Birnbaum–Saunders (BS) distribution, which is asymmetrical and has shown to be a good alternative for describing medical data. Inference based on the maximum likelihood method and a type of residual are derived for the tobit–BS model. We perform global and local influence diagnostics to assess the sensitivity of the maximum likelihood estimators to atypical cases. A Monte Carlo simulation study is carried out to empirically evaluate the performance of these estimators. We conduct a data analysis for the mentioned application of measles vaccine based on the proposed model with the help of the R software. The results show the good performance of the tobit–BS model.     

A flexible semiparametric regression model for bimodal,asymmetric and censored data

In this paper, we propose a new semiparametric heteroscedastic regression model allowing for positive and negative skewness and bimodal shapes using the B-spline basis for nonlinear effects. The proposed distribution is based on the generalized additive models for location, scale and shape framework in order to model any or all parameters of the distribution using parametric linear and/or nonparametric smooth functions of explanatory variables. We motivate the new model by means of Monte Carlo simulations, thus ignoring the skewness and bimodality of the random errors in semiparametric regression models, which may introduce biases on the parameter estimates and/or on the estimation of the associated variability measures. An iterative estimation process and some diagnostic methods are investigated. Applications to two real data sets are presented and the method is compared to the usual regression methods.