  In this paper, we propose a nonparametric Bayesian approach for Lindsey and
penalized Gaussian mixtures methods. We compare these methods with the
Dirichlet process mixture model. Our approach is a Bayesian nonparametric
method not based solely on a parametric family of probability distributions.
Thus, the fitted models are more robust to model misspecification. Also, with
the Bayesian approach, we have the entire posterior distribution of our
parameter of interest; it can be summarized through credible intervals, mean,
median, standard deviation, quantiles, etc. The Lindsey, penalized Gaussian
mixtures, and Dirichlet process mixture methods are reviewed. The estimations
are performed via Markov chain Monte Carlo (MCMC) methods. The penalized
Gaussian mixtures method is implemented via Hamiltonian Monte Carlo (HMC). We
show that under certain regularity conditions, and as n increases, the
posterior distribution of the weights converges to a Normal distribution.
Simulation results and data analysis are reported.
