Consistency of \(L_ p\)-best monotone approximations

DOI10.1016/0378-3758(94)00144-KzbMath0839.62049OpenAlexW2051527039MaRDI QIDQ1907638

Carlos Matrán, Juan Antonio Cuesta-Albertos, J. Santos Domínguez-Menchero

Publication date: 23 June 1996

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0378-3758(94)00144-k

zbMATH Keywords

regression functionconsistency propertieskernel regression estimatealmost sure consistencyLp-best monotone approximationLp-consistencyLp-Dip

Mathematics Subject Classification ID

Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Strong limit theorems (60F15)

Related Items (6)

New designs to consistently estimate the isotonic regression ⋮ On the estimation of monotone uniform approximations ⋮ A note on estimating a smooth monotone regression by combining kernel and density estimates ⋮ AnL₂point of view in testing monotone regression ⋮ Analyzing an extension of the isotonic regression problem ⋮ On minimizing sequences for \(k\)-centres

Cites Work

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• Conditional bounds and best \(L_{\infty}\)-approximations in probability spaces
• Best \(L_ 1\)-approximation of quasi continuous functions on [0,1 by nondecreasing functions]
• Distribution-free consistency results in nonparametric discrimination and regression function estimation
• Estimating a smooth monotone regression function
• Isotone optimization. II
• Some stochastics on monotone functions

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