A life distribution function F is said to be star-shaped if F(x)/x is nondecreasing on its support. This generalizes the model of a convex distribution function, even allowing for jumps. The nonparametric maximum likelihood estimation is known to be inconsistent. We provide a uniformly strongly consistent least squares estimator. We also derive the convergence in distribution of the estimator at a point where F(x)/x is increasing using the arg max theorem.
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