Ridge regression with adaptive additive rectangles and other piecewise functional templates

Functional Additive Regression

We suggest a new method, called Functional Additive Regression, or FAR, for efficiently performing high dimensional functional regression. FAR extends the usual linear regression model involving a functional predictor, X(t), and a scalar response, Y , in two key respects. First, FAR uses a penalized least squares optimization approach to efficiently deal with high dimensional problems involving...

Adaptive Ridge Regression for Rare Variant Detection

It is widely believed that both common and rare variants contribute to the risks of common diseases or complex traits and the cumulative effects of multiple rare variants can explain a significant proportion of trait variances. Advances in high-throughput DNA sequencing technologies allow us to genotype rare causal variants and investigate the effects of such rare variants on complex traits. We...

Beyond unimodal regression: modelling multimodality with piecewise unimodal, mixture or additive regression

Research in the field of nonparametric shape constrained regression has been extensive and there is need for such methods in various application areas, since shape constraints can reflect prior knowledge about the underlying relationship. It is, for example, often natural that some intensity first increases and then decreases over time, which can be described by a unimodal shape constraint. But...

Functional Regression and Adaptive Control

Adaptive functional linear regression

We consider the estimation of the slope function in functional linear regression, where scalar responses are modeled in dependence of random functions. Cardot and Johannes [2010] have shown that a thresholded projection estimator can attain up to a constant minimax-rates of convergence in a general framework which allows to cover the prediction problem with respect to the mean squared predictio...