Monotone nonparametric regression. (English) Zbl 0647.62042

Mukerjee, Hari

Ann. Stat. 16, No. 2, 741-750 (1988).

Summary: In monotone regression procedures one utilizes only the monotonicity of the regression function. In nonparametric regression one utilizes only the assumed smoothness. The analytic and asymptotic properties of the estimator are superior in the latter case; however, monotonicity is not guaranteed. We study a hybrid procedure that produces monotone estimators with properties similar to those of nonparametric regression estimators.

MSC:

62G05	Nonparametric estimation
62E20	Asymptotic distribution theory in statistics
60F05	Central limit and other weak theorems
60F15	Strong limit theorems

Keywords:

order statistic; uniform strong consistency; isotonic regression; asymptotic normality; monotone regression procedures; hybrid procedure; monotone estimators; nonparametric regression estimators