An Algorithm for Computing the Nonparametric MLE of a Mixing Distribution
提出一种快速算法，用于计算混合模型中混合分布的非参数最大似然估计，适用于半参数问题中轮廓似然的计算。
Abstract A fast algorithm for calculating the nonparametric maximum likelihood estimate (MLE) of a mixing distribution, G(·). in a mixture model is discussed. The literature contains several methods for computing the nonparametric MLE of G, but these methods are slow. In this article we develop an algorithm for maximizing the log-likelihood l(G) over the family ℊ, of all distribution functions, that yields the nonparametric MLE of G. In some semiparametric problems, a structural or fixed parameter β is of interest, and we are interested in computing profile likelihood, sup Gl(G, β), for a grid of values of β. The algorithm that we propose is fast enough for this purpose. Examples illustrate and compare the algorithms; one taken from an article by Laird, the common mean problem, and one taken from the literature on optimal experimental design. It is also noted that routines from the literature on semi-infinite programming may be used to compute the profile log-likelihood.