Monotone Percentile Regression

Penalized wavelet monotone regression

In this paper we focus on nonparametric estimation of a constrained regression function using penalized wavelet regression techniques. This results into a convex optimization problem under linear constraints. Necessary and sufficient conditions for existence of a unique solution are discussed. The estimator is easily obtained via the dual formulation of the optimization problem. In particular w...

Adaptive Monotone Shrinkage for Regression

We develop an adaptive monotone shrinkage estimator for regression models with the following characteristics: i) dense coefficients with small but important effects; ii) a priori ordering that indicates the probable predictive importance of the features. We capture both properties with an empirical Bayes estimator that shrinks coefficients monotonically with respect to their anticipated importa...

Simultaneous confidence bands for a percentile line in linear regression

Construction of simultaneous confidence bands for a percentile line in linear regression has been considered by several authors. But only conservative symmetric bands, which use critical constants over the whole covariate range (−∞, ∞), are available in the literature. New methods allow the construction of exact symmetric bands for a percentile line over a finite interval of the covariate x. Th...

Calibrated Percentile Double Bootstrap for Robust Linear Regression Inference

Forward stagewise regression and the monotone lasso

Abstract: We consider the least angle regression and forward stagewise algorithms for solving penalized least squares regression problems. In Efron, Hastie, Johnstone & Tibshirani (2004) it is proved that the least angle regression algorithm, with a small modification, solves the lasso regression problem. Here we give an analogous result for incremental forward stagewise regression, showing tha...