A least squares-type density estimator using a polynomial function

Abstract Higher-order density approximation and estimation methods using orthogonal series expansion have been extensively discussed in statistical literature and its various fields of application. This study proposes least squares-type estimation for series expansion via minimizing the weighted square difference of series distribution expansion and a benchmarking distribution estimator. As the least squares-type estimator has an explicit expression, similar to the classical moment-matching technique, its asymptotic properties are easily obtained under certain regularity conditions. In addition, we resolve the non-negativity issue of the series expansion using quadratic programming. Numerical examples with various simulated and real datasets demonstrate the superiority of the proposed estimator.