Variable selection in saturated and supersaturated designs via lp-lq minimization

Buccini A.;De la Cruz Cabrera O.;Koukouvinos C.

;Mitrouli M.;Reichel L.

2021-01-01

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Abstract

In many real world problems it is of interest to ascertain which factors are most relevant for determining a given outcome. This is the so-called variable selection problem. The present paper proposes a new regression model for its solution. We show that the proposed model satisfies continuity, sparsity, and unbiasedness properties. A generalized Krylov subspace method for the practical solution of the minimization problem involved is described. This method can be used for the solution of both small-scale and large-scale problems. Several computed examples illustrate the good performance of the proposed model. We place special focus on screening studies using saturated and supersaturated experimental designs.