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Limit Theory in Monotone Function Estimation. / Durot, Cécile; Lopuhaa, Hendrik P.

In: Statistical Science, Vol. 33, No. 4, 2018, p. 547-567.

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Durot, C & Lopuhaa, HP 2018, 'Limit Theory in Monotone Function Estimation' Statistical Science, vol. 33, no. 4, pp. 547-567. https://doi.org/10.1214/18-STS664

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Durot, Cécile ; Lopuhaa, Hendrik P. / Limit Theory in Monotone Function Estimation. In: Statistical Science. 2018 ; Vol. 33, No. 4. pp. 547-567.

BibTeX

@article{95f1cb4bbb91467187962d54b9fd7c94,
title = "Limit Theory in Monotone Function Estimation",
abstract = "Abstract. We give an overview of the different concepts and methods thatare commonly used when studying the asymptotic properties of isotonic estimators.After introducing the inverse process, we illustrate its use in establishingweak convergence of the estimators at a fixed point and also weakconvergence of global distances, such as the Lp-distance and supremum distance.Furthermore, we discuss the developments on smooth isotonic estimation.",
keywords = "Cox model, current status model, isotonic estimation, limit theory, Lp-distance, maximum likelihood estimators, monotone density, monotone failure rate, monotone regression, supremum distance",
author = "C{\'e}cile Durot and Lopuhaa, {Hendrik P.}",
year = "2018",
doi = "10.1214/18-STS664",
language = "English",
volume = "33",
pages = "547--567",
journal = "Statistical Science",
issn = "0883-4237",
publisher = "Institute of Mathematical Statistics",
number = "4",

}

RIS

TY - JOUR

T1 - Limit Theory in Monotone Function Estimation

AU - Durot, Cécile

AU - Lopuhaa, Hendrik P.

PY - 2018

Y1 - 2018

N2 - Abstract. We give an overview of the different concepts and methods thatare commonly used when studying the asymptotic properties of isotonic estimators.After introducing the inverse process, we illustrate its use in establishingweak convergence of the estimators at a fixed point and also weakconvergence of global distances, such as the Lp-distance and supremum distance.Furthermore, we discuss the developments on smooth isotonic estimation.

AB - Abstract. We give an overview of the different concepts and methods thatare commonly used when studying the asymptotic properties of isotonic estimators.After introducing the inverse process, we illustrate its use in establishingweak convergence of the estimators at a fixed point and also weakconvergence of global distances, such as the Lp-distance and supremum distance.Furthermore, we discuss the developments on smooth isotonic estimation.

KW - Cox model

KW - current status model

KW - isotonic estimation

KW - limit theory

KW - Lp-distance

KW - maximum likelihood estimators

KW - monotone density

KW - monotone failure rate

KW - monotone regression

KW - supremum distance

U2 - 10.1214/18-STS664

DO - 10.1214/18-STS664

M3 - Article

VL - 33

SP - 547

EP - 567

JO - Statistical Science

T2 - Statistical Science

JF - Statistical Science

SN - 0883-4237

IS - 4

ER -

ID: 48040150