Penalized likelihood regression for generalized linear models with non-quadratic penalties

被引:63
作者
Antoniadis, Anestis [1 ]
Gijbels, Irene [2 ]
Nikolova, Mila [3 ]
机构
[1] Univ Grenoble 1, Dept Stat, Lab Jean Kuntzmann, Tour IRMA, F-38041 Grenoble 9, France
[2] Katholieke Univ Leuven, Dept Math, Leuven Stat Res Ctr LStat, B-3001 Louvain, Belgium
[3] PRES UniverSud, CNRS ENS Cachan, Ctr Math & Leurs Applicat, F-94235 Cachan, France
关键词
Denoising; Edge-detection; Generalized linear models; Non-parametric regression; Non-convex analysis; Non-smooth analysis; Regularized estimation; Smoothing; Thresholding; FREE-KNOT SPLINES; LEAST-SQUARES; NONCONVEX REGULARIZATION; ASYMPTOTIC ANALYSIS; WAVELET SHRINKAGE; ORACLE PROPERTIES; IMAGE RECOVERY; EARLY VISION; SELECTION; LASSO;
D O I
10.1007/s10463-009-0242-4
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
One of the popular method for fitting a regression function is regularization: minimizing an objective function which enforces a roughness penalty in addition to coherence with the data. This is the case when formulating penalized likelihood regression for exponential families. Most of the smoothing methods employ quadratic penalties, leading to linear estimates, and are in general incapable of recovering discontinuities or other important attributes in the regression function. In contrast, non-linear estimates are generally more accurate. In this paper, we focus on non-parametric penalized likelihood regression methods using splines and a variety of non-quadratic penalties, pointing out common basic principles. We present an asymptotic analysis of convergence rates that justifies the approach. We report on a simulation study including comparisons between our method and some existing ones. We illustrate our approach with an application to Poisson non-parametric regression modeling of frequency counts of reported acquired immune deficiency syndrome (AIDS) cases in the UK.
引用
收藏
页码:585 / 615
页数:31
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