Nonparametric estimation of density and hazard rate functions with shape restrictions

摘要: Methods for nonparametric maximum likelihood estimation of probability distributions are presented, with assumptions concerning the smoothness and shape. In particular, decreasing density is considered, as well constraints on hazard function including increasing, convex or bathtub-shaped, increasing convex. Regression splines used to formulate problem in terms programming, iteratively re-weighted least squares cone projection algorithms proposed. The estimators obtain convergence rate r=(p+1)/(2p+3) where p degree polynomial spline. method can be right-censored data. These methods applied real simulated data sets illustrate small sample properties compare existing estimators.