Variable selection in multiple regression with random design

We consider least-squares regression using a randomly generated subspace G P ⊂ F of finite dimen- sion P, where F is a function space of infinite dimension, e.g.. G P is defined as

(2011), who used a fixed number of extreme conditional quantile estimators to estimate the conditional tail index, for instance using the Hill (Hill, 1975) and Pickands (Pickands,

We also considered mice: we applied logistic regression with a classical forward selection method, with the BIC calculated on each imputed data set. However, note that there is

The literature on this issue, corresponding to step (a), covers three main ways to perform the selection: the first one is to consider all possible subsets, leading to an

Keywords and phrases: Nonparametric regression, Least-squares estimators, Penalized criteria, Minimax rates, Besov spaces, Model selection, Adaptive estimation.. ∗ The author wishes

We see that CorReg , used as a pre-treatment, provides similar prediction accuracy as the three variable selection methods (this prediction is often better for small datasets) but

Literature on this topic started with stepwise regression (Breaux 1967) and autometrics (Hendry and Richard 1987), moving to more advanced procedures from which the most famous are

Introduced by Friedman (1991) the Multivariate Adaptive Regression Splines is a method for building non-parametric fully non-linear ANOVA sparse models (39). The β are parameters