Method of Moments with Unknown Distribution Form

In this paper we consider the method of moments with unknown distribution form. Assume that the distribution function F_θ（x） can be expressed or approached by a polynomial with unknown power r and parameters θ₁; …,θ_r are involved as the coefficients. We develop a new method of moments to estimate the parameters θ₁,…,θ_r and find the r automatically. The estimates are strong consistent.