Rosnel Sessinou

phd seminar

Rosnel Sessinou

AMSE
Precision least squares: Estimation and inference in high-dimensional linear regression models
Joint with
Luca Margaritella
Venue

MEGA Salle de conf

MEGA - Salle de conférence

Maison de l'économie et de la gestion d'Aix
424 chemin du viaduc
13080 Aix-en-Provence

Date(s)
Tuesday, September 21 2021| 11:00am to 11:45am
Contact(s)

Kenza Elass: kenza.elass[at]univ-amu.fr
Camille Hainnaux: camille.hainnaux[at]univ-amu.fr
Daniela Horta Saenz: daniela.horta-saenz[at]univ-amu.fr
Jade Ponsard: jade.ponsard[at]univ-amu.fr

Abstract

The least square estimator can be shown to depend only on a single parameter, the precision matrix. We show that a regularized estimate of the precision matrix can be directly used to obtain the least square solution even when the number of covariates can be strictly larger than the sample size. As biases can occur from different choices of the precision matrix estimate, we show how to construct a (nearly) unbiased estimator irrespectively of the sparsity within the data generating process. We call this estimator the Precision Least Squares (PrLS). Assuming stationarity for the covariates and the error process we show that the PrLS estimator is (i) asymptotically Gaussian, (ii) automatically free of the usual regularization bias. As an application, we employ the Precision Least Squares to estimate the predictive connectedness among daily asset returns of 88 global banks. We show that financial crisis corresponds to a collapse of financial linkage in line with two financial theory predictions.