A filtered polynomial approach to density estimation (Q626213)

Density estimation is considered, based on the representation \(f(x)=h(t(x))t'(x)\), where \(h\) is some fixed density, and \(t(x)\) is a monotonically increasing transformation. The transformation \(t\) is approximated by a monotonic polynomial. A maximum likelihood approach is used to fit the model to the data. An algorithm for the estimation is described which uses a special representation of monotone polynomials and a modified Newton-Raphson method of minimization. Applications to real life data sets are presented.