Abstract
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.
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 language | English |
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Pages (from-to) | 1031-1098 |
Number of pages | 68 |
Journal | Electronic Journal of Statistics |
Volume | 13 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2019 |
Keywords
- Kernel estimator
- Lp loss
- central limit theorem
- smoothed Grenander-type estimator
- isotonized kernel estimator
- boundary corrections
- Hellinger loss
- testing monotonicity