Asymptotic normality of the \(L_k\)-error of the Grenander estimator

DOI10.1214/009053605000000462zbMath1086.62063arXivmath/0602244OpenAlexW2949397395MaRDI QIDQ2368852

Vladimir N. Kulikov, Hendrik P. Lopuhaä

Publication date: 28 April 2006

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0602244

zbMATH Keywords

central limit theoremmonotone densityconcave majorantisotonic estimationBrownian motion with quadratic drift

Mathematics Subject Classification ID

Density estimation (62G07) Asymptotic distribution theory in statistics (62E20) Asymptotic properties of nonparametric inference (62G20) Central limit and other weak theorems (60F05)

Related Items (19)

Berry-Esseen bounds for Chernoff-type nonstandard asymptotics in isotonic regression ⋮ On the \(\mathbb L_p\)-error of monotonicity constrained estimators ⋮ On the L_p error of the Grenander‐type estimator in the Cox model ⋮ Estimating the Upper Support Point in Deconvolution ⋮ Coverage of credible intervals in Bayesian multivariate isotonic regression ⋮ Posterior contraction and testing for multivariate isotonic regression ⋮ A central limit theorem for the Hellinger loss of Grenander‐type estimators ⋮ A Bernstein-type estimator for decreasing density with application to \(p\)-value adjustments ⋮ The distribution of the maximal difference between a Brownian bridge and its concave majorant ⋮ Adaptivity and optimality of the monotone least-squares estimator ⋮ Distribution of global measures of deviation between the empirical distribution function and its concave majorant ⋮ Limit theory in monotone function estimation ⋮ Uniform central limit theorems for the Grenander estimator ⋮ Limit distribution theory for block estimators in multiple isotonic regression ⋮ The limit distribution of the \(L_{\infty}\)-error of Grenander-type estimators ⋮ The behavior of the NPMLE of a decreasing density near the boundaries of the support ⋮ Monotone nonparametric regression with random design ⋮ Nonparametric estimation of a regression function from backward recurrence times in a cross-sectional sampling ⋮ Testing equality of functions under monotonicity constraints

Cites Work

• Cube root asymptotics
• Asymptotic normality of the \(L_1\) error of the Grenander estimator
• Sharp asymptotics for isotonic regression
• Adaptive smoothing for a penalized NPMLE of a non-increasing density
• The behavior of the NPMLE of a decreasing density near the boundaries of the support
• An approximation of partial sums of independent RV'-s, and the sample DF. I
• Convergence of stochastic processes
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