Seminar

Estimation of the density of random coefficients when the regressors have limited variation

Eric Gautier ( Toulouse School of Economics)

December 8, 2016, 11:00–12:15

Toulouse

Room MS 003

MAD-Stat. Seminar

Abstract

We consider a linear model where the coefficients - intercept and slopes - are random and independent from regressors which support is a proper subset. We provide conditions for identification of the distribution of the coefficients relying on quasi-analyticity. Some involve the tails of the intercept and slopes allowing for discrete regressors and multiple nonlinear transformations, others only involve the tails of the slopes and continuous but possibly bounded regressors. Lower bounds on the minimax risk for the estimation of the density are derived in this model and a related white noise model. We present estimators which involve: series based estimation of the partial Fourier transform of the density relative to the intercept, interpolation around zero, and partial Fourier inversion, and give rates of convergence under smoothness and tail assumptions. A data-driven rule delivers adaptive estimators.