Regularization of nonparametric frontier estimators

On aggregation of nonparametric estimators

We study the problem of aggregation of arbitrary estimators from a given family F with respect to Lp–risks. The proposed method is based on comparison of empirical estimates of certain linear functionals with estimates induced by the family F . We derive oracle inequalities and show that they are unimprovable in some sense. Short Title: Aggregation of nonparametric estimators

Nonparametric learning and Regularization

Several nonparametric methods in a regression model are presented. First, the most classical ones: piecewise polynomial estimators, estimation with Spline bases, kernel estimators and projection estimators on orthonormal bases (such as Fourier or wavelet bases). Since these methods suffer from the curse of dimensionality, we also present Generalized Additive Models and CART regression models. T...

Nonparametric sparsity and regularization

In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric model, hence avoiding linear or additive models. The key idea is to measure the importance of each variable in the model by making use of partial derivatives...

Nonparametric Regularization of Decision Trees

Efficient Frontier - Comparing Different Volatility Estimators

Abstract—Modern Portfolio Theory (MPT) according to Markowitz states that investors form mean-variance efficient portfolios which maximizes their utility. Markowitz proposed the standard deviation as a simple measure for portfolio risk and the lower semi-variance as the only risk measure of interest to rational investors. This paper uses a third volatility estimator based on intraday data and c...