Christine De Mol

TL;DR: It is proved that replacing the usual quadratic regularizing penalties by weighted 𝓁p‐penalized penalties on the coefficients of such expansions, with 1 ≤ p ≤ 2, still regularizes the problem.

Abstract: We consider linear inverse problems where the solution is assumed to have a sparse expansion on an arbitrary pre-assigned orthonormal basis. We prove that replacing the usual quadratic regularizing penalties by weighted l^p-penalties on the coefficients of such expansions, with 1 < or = p < or =2, still regularizes the problem. If p < 2, regularized solutions of such l^p-penalized problems will have sparser expansions, with respect to the basis under consideration. To compute the corresponding regularized solutions we propose an iterative algorithm that amounts to a Landweber iteration with thresholding (or nonlinear shrinkage) applied at each iteration step. We prove that this algorithm converges in norm. We also review some potential applications of this method.

TL;DR: This work proposes to add to the objective function a penalty proportional to the sum of the absolute values of the portfolio weights, which regularizes (stabilizes) the optimization problem, encourages sparse portfolios, and allows accounting for transaction costs.

TL;DR: In this article, the authors consider Bayesian regression with normal and double-exponential priors as forecasting methods based on large panels of time series and show that these forecasts are highly correlated with principal component forecasts and that they perform equally well for a wide range of prior choices.

TL;DR: In this article, the authors consider Bayesian regression with normal and double-exponential priors as forecasting methods based on large panels of time series and show that these forecasts are highly correlated with principal component forecasts and that they perform equally well for a wide range of prior choices.