Monotone Median 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...

Least Median of Squares Regression

Classical least squares regression consists of minimizing the sum of the squared residuals. Many authors have produced more robust versions of this estimator by replacing the square by something else, such as the absolute value. In this article a different approach is introduced in which the sum is replaced by the median of the squared residuals. The resulting estimator can resist the effect of...

Isotonic Median Regression via Scaling

This paper gives algorithms for determining isotonic median regressions (i.e., isotonic regression using the L1 metric) satisfying order constraints given by various ordered sets. For a rooted tree the regression can be found in Θ(n log n) time, while for a star it can be found in Θ(n) time, where n is the number of vertices. For bivariate data, when the set is a grid the regression can be foun...

Robust PLS regression based on simple least median squares regression