Abstract
We consider Grenander-type estimators for a monotone function (Formula presented.), obtained as the slope of a concave (convex) estimate of the primitive of λ. Our main result is a central limit theorem for the Hellinger loss, which applies to estimation of a probability density, a regression function or a failure rate. In the case of density estimation, the limiting variance of the Hellinger loss turns out to be independent of λ.
Original language | English |
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Pages (from-to) | 180-196 |
Number of pages | 17 |
Journal | Statistica Neerlandica |
Volume | 73 (2019) |
Issue number | 2 |
DOIs | |
Publication status | Published - 2018 |
Keywords
- central limit theorem
- Grenander estimator
- Hellinger distance
- isotonic estimation