Density Estimation Using Exponentials of Orthogonal Series
Abstract If a density is represented as an exponential of a series of orthogonal polynomials, it has a simple likelihood with a complete set of sufficient statistics. To ensure that the maximum likelihood equations are well conditioned, the polynomials should be orthogonal with respect to the estimated density. The optimal number of terms in the series can be determined by minimizing an estimate of a loss function. The penalized likelihood equations can be solved with little extra effort. Computer simulations show that the resulting density estimator has a smaller mean integrated squared error than the linear orthogonal series estimator.