Mean-shift least squares model averaging

TL;DR

This paper introduces the mean-shift Mallows model average (MSA) estimator, which improves model averaging by controlling bias and error, and demonstrates its asymptotic optimality and superior performance over existing methods.

Contribution

It proposes a novel MSA estimator that extends the MMA approach by jointly controlling bias and error, achieving asymptotic optimality.

Findings

MSA estimator outperforms MMA in simulations

MSA is asymptotically optimal in mean squared error

Proposed method effectively controls bias and regression error

Abstract

This paper proposes a new estimator for selecting weights to average over least squares estimates obtained from a set of models. Our proposed estimator builds on the Mallows model average (MMA) estimator of Hansen (2007), but, unlike MMA, simultaneously controls for location bias and regression error through a common constant. We show that our proposed estimator-- the mean-shift Mallows model average (MSA) estimator-- is asymptotically optimal to the original MMA estimator in terms of mean squared error. A simulation study is presented, where we show that our proposed estimator uniformly outperforms the MMA estimator.