On the choice of high-dimensional regression parameters in Gaussian random tomography

Abstract The stochastic Radon transform was introduced by Panaretos in order to estimate a biophysical particle, modelled as a three-dimensional probability density subject to random and unknown rotations before being projected onto the imaging plane. Assuming that the particle has a Gaussian mixture distribution, the question arises as to how to recover the modes of the mixture, and the mixing weights. Panaretos and Konis proposed to do this in a sequential manner, using high-dimensional regression. Their approach has two drawbacks: first, the mixing weight estimates often have incorrect rank; second, much information inherent in the coefficients from the penalized regression approach (Lasso, or more generally elastic net) is lost. We propose a procedure, based on the asymptotic precision matrix, that exploits the information from the high-dimensional regression more efficiently, and yields in particular a method for choosing the parameter that balances the Lasso with ridge regression.