Penalized Log-Density Estimation Using Legendre Polynomials
Compute basic values
compute_fitted
Compute lambda sequence
Fit plde for a fixed tuning parameter
Fit plde for a fixed tuning parameter
legendre_polynomial
Minimization of the quadratic approximation to objective function
Optimal model selection
Penalized Log-density Estimation Using Legendre Polynomials
Compute quadratic approximation objective function
Soft thresholding operator
Update the Legendre polynomial coefficient vector
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).