An experiment records stimulus and response for a random sample of cases. The relationship between response and stimulus is thought to be linear, the values of the slope and intercept varying by case. From such data, we construct a consistent, asymptotically normal, nonparametric estimator for the joint density of the slope and intercept. Our methodology incorporates the radial projection-slice theorem for the Radon transform, a technique for locally linear nonparametric regression and a tapered Fourier inversion. Computationally, the new density estimator is more feasible than competing nonparametric estimators, one of which is based on moments and the other on minimum distance considerations.
"On nonparametric estimation of intercept and slope distributions in random coefficient regression." Ann. Statist. 24 (6) 2569 - 2592, December 1996. https://doi.org/10.1214/aos/1032181170