基于径向基的自适应惩罚样条回归模型

传统惩罚样条回归模型中惩罚项的设置未考虑数据的空间异质性,因而对复杂数据的拟合缺乏自适应性.文章通过对径向基函数的几何意义分析,以节点两侧相邻区域内数据点的纵向极差为基础,构造局部惩罚权重向量并加入到约束回归模型的惩罚项中,构造了基于径向基的自适应惩罚样条回归模型.新模型在观测数据波动较大的区域,给予拟合曲线较小的惩罚,而在观测数据波动较小的区域,给予拟合曲线较大的惩罚,从而使拟合曲线能自适应地反映观测数据的局部变化特征.模拟和应用结果显示新模型的拟合效果显著优于传统的惩罚样条回归模型.     

C^3连续的保形插值三角样本曲线

本给出了构造保形插值曲线的三角样条方法，即在每两个型值点之间构造两段三次参数三角样条曲线。所构造的插值曲线是局部的，保形的和C^3连续的而且曲线的形状可由参数调节。     

HAZARD REGRESSION WITH PENALIZED SPLINE: THE SMOOTHING PARAMETER CHOICE AND ASYMPTOTICS

In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establish the consistency and the asymptotic normality of the penalized likelihood estimators. Numerical studies and an example are conducted to evaluate the performances of the new procedure.     

Hazard regression with penalized spline: The smoothing parameter choice and asymptotics

In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establish the consistency and the asymptotic normality of the penalized likelihood estimators. Numerical studies and an example are conducted to evaluate the performances of the new procedure.     

Estimation spline de quantiles conditionnels pour variables explicatives fonctionnelles

This Note deals with a linear model of regression on quantiles with the explanatory variable taking values in some functional space and a scalar response. We propose a spline estimator of the functional coefficient that minimizes a penalized L¹ type criterion (the penalization is of primary importance to get existence and convergence of the estimator), then we study the asymptotic behaviour of this estimator. To cite this article: H. Cardot et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

纵向数据边际模型非参数光滑方法的比较

对于纵向数据边际模型的均值函数, 有很多非参数估计方法, 其中回归样条, 光滑样条, 似乎不相关(SUR)核估计等方法在工作协方差阵正确指定时具有最小的渐近方差. 回归样条的渐近偏差与工作协方差阵无关, 而SUR核估计和光滑样条估计的渐近偏差却依赖于工作协方差阵. 本文主要研究了回归样条, 光滑样条和SUR核估计的效率问题. 通过模拟比较发现回归样条估计的表现比较稳定, 在大多数情况下比光滑样条估计和SUR核估计的效率高.     

半参数广义线性混合效应模型的影响分析

本文把随机效应当作是缺失数据并利用P-样条拟合非参数部分,从而得到了半参数广义线性混合效应模型(GPLMM)的MCNR估计算法;同时利用Q-函数,我们得到了模型的参数部分的广义Cook距离以及非参数部分的广义DFIT,此外,本文还研究了四种不同扰动情形的PLMM的局部影响分析,得到了相应的影响矩阵,最后,我们通过—个实际例子验证了所提出的诊断统计量的有效性。     

Robust penalized regression spline fitting with application to additive mixed modeling

An increasingly popular method for smoothing noisy data is penalized regression spline fitting. In this paper a new procedure is proposed for fitting robust penalized regression splines. This procedure is computationally fast, straightforward to implement, and can be paired with any smoothing parameter selection method. In addition, it can also be extended to other settings, such as additive mixed modeling. Both simulated and real data examples are used to illustrate the effectiveness of the procedure.     

Estimation of Smooth Time-Varying Parameters in State Space Models

In this article, we propose a penalized likelihood method to estimate time-varying parameters in standard linear state space models. The time-varying parameter is modeled as a smoothing spline and then expressed as a state space model. The maximum likelihood method is used to estimate the smoothing parameter. The proposed method is assessed by a simulation study and applied to virological response data from an HIV-infected patient receiving antiretroviral treatment.     

Nonparametric Regression on a Graph

The ‘Signal plus Noise’ model for nonparametric regression can be extended to the case of observations taken at the vertices of a graph. This model includes many familiar regression problems. This article discusses the use of the edges of a graph to measure roughness in penalized regression. Distance between estimate and observation is measured at every vertex in the L₂ norm, and roughness is penalized on every edge in the L₁ norm. Thus the ideas of total variation penalization can be extended to a graph. The resulting minimization problem presents special computational challenges, so we describe a new and fast algorithm and demonstrate its use with examples.

The examples include image analysis, a simulation applicable to discrete spatial variation, and classification. In our examples, penalized regression improves upon kernel smoothing in terms of identifying local extreme values on planar graphs. In all examples we use fully automatic procedures for setting the smoothing parameters. Supplemental materials are available online.