Penalized Log-Density Estimation Using Legendre Polynomials
Description
We present a penalized log-density estimation method using Legendre polynomials with lasso penalty to adjust estimate's smoothness. Re-expressing the logarithm of the density estimator via a linear combination of Legendre polynomials, we can estimate parameters by maximizing the penalized log-likelihood function. Besides, we proposed an implementation strategy that builds on the coordinate decent algorithm, together with the Bayesian information criterion (BIC).