We investigate the asymptotic behavior of the Lp-distance between
a monotone function on a compact interval and a smooth estimator
of this function. Our main result is a central limit theorem for the Lp-error
of smooth isotonic estimators obtained by smoothing a Grenander-type
estimator or isotonizing the ordinary kernel estimator. As a preliminary result
we establish a similar result for ordinary kernel estimators. Our results
are obtained in a general setting, which includes estimation of a monotone
density, regression function and hazard rate. We also perform a simulation
study for testing monotonicity on the basis of the L2-distance between the
kernel estimator and the smoothed Grenander-type estimator.
Original languageEnglish
Pages (from-to)1031-1098
Number of pages68
JournalElectronic Journal of Statistics
Issue number1
Publication statusPublished - 2019

    Research areas

  • Kernel estimator, Lp loss, central limit theorem, smoothed Grenander-type estimator, isotonized kernel estimator, boundary corrections, Hellinger loss, testing monotonicity

ID: 53161420