Constrained regularized regression model search in large sets of regressors

Abstract

We consider the problem of regression estimation under a complex of additional assumptions. First, the regression coefficients are assumed to be doubly constrained by individual non-negativity inequalities along with the unit-sum equality. Second, it is assumed that the number of regressors far exceeds that of samples. An additional assumption is that the regression coefficients differ from zero only within a really existing small subset of a large universe of regressors, and the search for this subset (Factor Search) is the main aim of data processing. The latter assumption ensues from the practical problem of recovering the hidden composition of an investment portfolio represented by a time series of its periodic returns (values of relative profitability). However, factor search, i.e., finding a small active subset among a huge set of correlated factors, is problematic unless some a priori information on the expected portfolio structure is available. We propose a regularized regression model based on the assumption that the portfolio under analysis is rationally composed by its administration.