Estimation of a function under shape restrictions. Applications to reliability

DOI10.1214/009053605000000138zbMath1072.62023arXivmath/0507427OpenAlexW1973521670MaRDI QIDQ2569243

Laurence Reboul

Publication date: 18 October 2005

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

Full work available at URL: https://arxiv.org/abs/math/0507427

zbMATH Keywords

adaptive estimationnonhomogeneous Poisson processhazard rateunimodal functiondata-driven estimatorU-shaped functionvariable binwidth histogram

Mathematics Subject Classification ID

Density estimation (62G07) Nonparametric estimation (62G05) Non-Markovian processes: estimation (62M09) Estimation in survival analysis and censored data (62N02)

Related Items (14)

Goodness of fit test for isotonic regression ⋮ Fusion of hard and soft information in nonparametric density estimation ⋮ On the \(\mathbb L_p\)-error of monotonicity constrained estimators ⋮ Testing \(k\)-monotonicity of a discrete distribution. Application to the estimation of the number of classes in a population ⋮ Nonparametric estimation of a convex bathtub-shaped hazard function ⋮ Efficient Bayesian shape-restricted function estimation with constrained Gaussian process priors ⋮ Nonparametric maximum likelihood computation of a \(U\)-shaped hazard function ⋮ A variable selection approach to monotonic regression with Bernstein polynomials ⋮ On Bayes inference for a bathtub failure rate via S-paths ⋮ Enforcing shape constraints on a probability density estimate using an additive adjustment curve ⋮ A refined Jensen's inequality in Hilbert spaces and empirical approximations ⋮ Computation of nonparametric convex hazard estimators via profile methods ⋮ Semiparametric regression with the U-shaped baseline hazard function in the additive hazards model under general censoring mechanisms ⋮ Goodness-of-Fit Test for Monotone Functions

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