A penalized maximum likelihood estimate of \(f(0+)\) when \(f\) is non- increasing. (English) Zbl 0822.62020

Woodroofe, Michael; Sun, Jiayang

Stat. Sin. 3, No. 2, 501-515 (1993).

Summary: The problem of estimating the value at \(0 +\) of a non-increasing density \(f\) (on \((0, \infty))\) is considered. It is shown, by example, that the problem is interesting, and it is noted that the nonparametric maximum likelihood estimator is inconsistent. A penalized maximum likelihood estimator is derived as an alternative, and its properties studied through simulations and asymptotic analysis. In particular, the penalized maximum likelihood estimator is shown to be consistent.

MSC:

62G05	Nonparametric estimation
62E20	Asymptotic distribution theory in statistics
62G20	Asymptotic properties of nonparametric inference

Keywords:

consistency; non-increasing density; nonparametric maximum likelihood estimator; penalized maximum likelihood estimator; simulations