Adaptive estimation in the linear random coefficients model when regressors have limited variation

par Eric Gautier (Université Toulouse 1, TSE)

vendredi 27 avr. 2018, 14:00 → 15:00 Europe/Paris

112 (Bât. Braconnier)

We consider a linear model where the coefficients - intercept and slopes - are random and independent from regressors which support is a proper (strict) subset. In this case the joint density of random coefficients is not identified. However, if we further assume that it has finite properly weighted L2 norm, it becomes identified. This is because certain partial Fourier transforms are analytic or quasi-analytic. Lower bounds on the supremum risk for the estimation of the density are derived for this model and a related white noise model. We present an estimator which involves: series based estimation of the partial Fourier transform of the density with respect to the intercept, interpolation around zero, and partial Fourier inversion. We give its rates of convergence and data-driven rules which deliver adaptive estimators.