On the rate of convergence of the maximum likelihood estimator of a \(k\)-monotone density
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Publication:1042977
DOI10.1007/s11425-009-0102-yzbMath1176.62031OpenAlexW2021974929WikidataQ34091226 ScholiaQ34091226MaRDI QIDQ1042977
Publication date: 7 December 2009
Published in: Science in China. Series A (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11425-009-0102-y
Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Applications of functional analysis in probability theory and statistics (46N30)
Related Items (8)
Fusion of hard and soft information in nonparametric density estimation ⋮ Bracketing numbers of convex and \(m\)-monotone functions on polytopes ⋮ Entropy of convex functions on \(\mathbb R^d\) ⋮ Minimax rates for conditional density estimation via empirical entropy ⋮ Uniform central limit theorems for the Grenander estimator ⋮ A two stage \(k\)-monotone B-spline regression estimator: uniform Lipschitz property and optimal convergence rate ⋮ How many Laplace transforms of probability measures are there? ⋮ On convex least squares estimation when the truth is linear
Cites Work
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- Multiply monotone functions and their Laplace transforms
- The Grenander estimator: A nonasymptotic approach
- Entropy estimate for \(k\)-monotone functions via small ball probability of integrated Brownian motions
- Weak convergence and empirical processes. With applications to statistics
- On estimating a density using Hellinger distance and some other strange facts
- Hellinger-consistency of certain nonparametric maximum likelihood estimators
- Estimation of a \(k\)-monotone density: limit distribution theory and the spline connection
- Entropy estimate for high-dimensional monotonic functions
- Metric entropy of high dimensional distributions
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