Testing for additivity with B-splines

Regression splines are often used for fitting nonparametric functions, and they work especially well for additivity models. In this paper, we consider two simple tests of additivity: an adaptation of Tukey's one degree of freedom test and a nonparametric version of Rao's score test. While the Tukey-type test can detect most forms of the local non-additivity at the parametric rate of O(n-1/2), the score test is consistent for all alternative at a nonparametric rate. The asymptotic distribution of these test statistics is derived under both the null and local alternative hypotheses. A simulation study is conducted to compare their finite-sample performances with some existing kernel-based tests. The score test is found to have a good overall performance.     

Local Dependence Test Between Random Vectors Based on the Robust Conditional Spearman’s ρ and Kendall’s τ

Acta Mathematicae Applicatae Sinica, English Series - This paper introduces two local conditional dependence matrices based on Spearman’s ρ and Kendall’s τ given the condition...     

Testing Lack-of-fit for a Polynomial Errors-in-variables Model

When a regression model is applied as an approximation of underlying model of data, the model checking is important and relevant. In this paper, we investigate the lack-of-fit test for a polynomial error-in-variables model. As the ordinary residuals are biased when there exist measurement errors in covariables,we correct them and then construct a residual-based test of score type. The constructed test is asymptotically chi-squared under null hypotheses. Simulation study shows that the test can maintain the significance level well.The choice of weight functions involved in the test statistic and the related power study are also investigated.The application to two examples is illustrated. The approach can be readily extended to handle more general models.     

Asymptotics of Huber-Dutter Estimators for Partial Linear Model with Nonstochastic Designs

For partial linear model Y=X~τβ_0 _(g0)(T) εwith unknown β_0∈R~d and an unknown smooth function go, this paper considers the Huber-Dutter estimators of β_0, scale σfor the errors and the function go respectively, in which the smoothing B-spline function is used. Under some regular conditions, it is shown that the Huber-Dutter estimators of β_0 and σare asymptotically normal with convergence rate n~((-1)/2) and the B-spline Huber-Dutter estimator of go achieves the optimal convergence rate in nonparametric regression. A simulation study demonstrates that the Huber-Dutter estimator of β_0 is competitive with its M-estimator without scale parameter and the ordinary least square estimator. An example is presented after the simulation study.     

以RDX为基的含铝炸药中铝粉粒度和氧化剂形态对加速金属能力的影响

利用激光速度干涉仪研究了含微米铝粉和纳米铝粉复合炸药加速金属平板的能力,结果表明纳米铝粉的引入能够获得更大的金属平板自由面速度,其反应时间比微米复合含铝炸药缩短35.1%。研究了氧化剂的形态对含铝炸药性能的影响,用物理化学手段获得的RDX/AP复合粒子复合粒子制作的含铝炸药加速金属平板的能力优于机械混合RDX/AP的含铝炸药,前者的反应时间也比后者短。此外,还研究了以富氧炸药取代RDX获得的含铝炸药的性能,结果表明其加速金属平板的速度比RDX/Al复合炸药提高10%。     

Efficient estimation for semiparametric varying- coefficient partially linear regression models with current status data

This article considers a semiparametric varying-coefficient partially linear regression model with current status data. The semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are conducted to examine the small-sample properties of the proposed estimates and a real dataset is used to illustrate our approach.     

一种快速稀疏分解图像去噪新方法*

提出了一种基于分层树型结构正交匹配追踪算法的快速图像去噪方法.通过选择高斯函数和墨西哥草帽小波母函数构建混合冗余字典,采用分层树状结构表示字典,结合构正交匹配追踪算法,实现图像稀疏表示,提高了图像表示的稀疏性,降低了算法的复杂度.依据噪音能量阈值,通过多次迭代达到图像去噪的目的.实验结果表明,在相同的噪音水平下,该迭代去噪算法取得了较高的较好的PSNR,获得更好的视觉效果.     

Robust Nonparametric Function Estimation for Errors-in-variables Models

This paper discusses robust nonparametric estimators of location regression function for errorsin-variables model with de-convolution kernel. The local constant smoother is used for the estimation of the nonparametric function, and the local linear smoother is proposed to deal with the boundary problem, as well as to improve the local constant smoother. We establish the asymptotic properties of the estimator, the influence function of the statistical functional and the breakdown point. A simulat...     

分段爆破地震强度的试验研究

在爆破实验中,通过调整段数、分段炸药量、炸药总量、间隔时间、孔网参数、岩石波阻等爆破相关因素,以改变各分段爆破地震波持续时间、段别间爆破地震波重叠程度来研究爆破地震强度与爆破相关因素间的相互关系。阐明了爆破地震波传播规律及其破坏行为特征,以及各个爆破相关因素对爆破地震强度的影响程度。获得了确定段数等爆破参数的规则,从而为生产实践设计最佳爆破参数提供理论依据。     

统计深度函数及其应用

次序统计量在一维统计数据分析中起着很重要的作用．多年来,人们一直在商维数据处理和分析中寻找“次序统计量”,却没有得到很满意的结果．由于缺少自然而有效的高维数据排序方法,因而象一维“中位数”的概念很难推广到高维．统计深度函数则提供了高维数据排序的一种工具,其主要思想是提供了一种从高维数据中心(最深点)向外的排序方法．不仅如此,统计深度函数已经在探索性高维数据分析,统计判决等方面带给我们一种全新的前景,并在工业、工程、生物医学等诸多领域得到很好的应用．本文介绍了统计深度函数概念及其应用,讨论了位置深度函数的标准,介绍了几种常用的统计深度函数．给出了由深度函数特别是由投影深度函数所诱导的位置和散布阵估计,介绍了它们的诸多优良性质,如极限分布,稳健性和有效性．由于在大多数场合下,高崩溃点的估计不是较有效的估计,而由统计深度函数所诱导的估计具有多元仿射不变性,并能提供理想的稳健性与有效性之间的平衡,本文还讨论了基于深度的统计检验和置信区域,介绍了统计深度函数的其他应用,如多元回归、带有变量误差模型、质量控制等,以及实际计算问题．指出了统计深度函数领域有关进一步的工作和研究方向．