Rosnel Sessinou

big data and econometrics seminar

Rosnel Sessinou

AMSE
Estimation and inference in high dimensional linear regression models
Venue

IBD Salle 21

Îlot Bernard du Bois - Salle 21

AMU - AMSE
5-9 boulevard Maurice Bourdet
13001 Marseille

Date(s)
Tuesday, September 28 2021| 2:00pm to 3:30pm
Contact(s)

Michel Lubrano: michel.lubrano[at]univ-amu.fr
Pierre Michel: pierre.michel[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 and (iii) control the directional false discovery rate. 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 financial theory predictions.