Minimax invariant estimator of a continuous distribution function

Qiqing Yu

doi:10.1007/BF00053401

Minimax invariant estimator of a continuous distribution function

Qiqing Yu

Mathematics and Statistics

Binghamton University

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Consider the problems of the continuous invariant estimation of a distribution function with a wide class of loss functions. It has been conjectured for long that the best invariant estimator is minimax for all sample sizes n≥1. This conjecture is proved in this short note.

Original language	English
Pages (from-to)	729-735
Number of pages	7
Journal	Annals of the Institute of Statistical Mathematics
Volume	44
Issue number	4
DOIs	https://doi.org/10.1007/BF00053401
State	Published - Dec 1992

Keywords

Lebesgue measure
Minimaxity
invariant estimator
nonparametric estimator
product measure
uniform distribution on a set

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10.1007/BF00053401

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title = "Minimax invariant estimator of a continuous distribution function",

abstract = "Consider the problems of the continuous invariant estimation of a distribution function with a wide class of loss functions. It has been conjectured for long that the best invariant estimator is minimax for all sample sizes n≥1. This conjecture is proved in this short note.",

keywords = "Lebesgue measure, Minimaxity, invariant estimator, nonparametric estimator, product measure, uniform distribution on a set",

author = "Qiqing Yu",

year = "1992",

month = dec,

doi = "10.1007/BF00053401",

language = "English",

volume = "44",

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journal = "Annals of the Institute of Statistical Mathematics",

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T1 - Minimax invariant estimator of a continuous distribution function

AU - Yu, Qiqing

PY - 1992/12

Y1 - 1992/12

N2 - Consider the problems of the continuous invariant estimation of a distribution function with a wide class of loss functions. It has been conjectured for long that the best invariant estimator is minimax for all sample sizes n≥1. This conjecture is proved in this short note.

AB - Consider the problems of the continuous invariant estimation of a distribution function with a wide class of loss functions. It has been conjectured for long that the best invariant estimator is minimax for all sample sizes n≥1. This conjecture is proved in this short note.

KW - Lebesgue measure

KW - Minimaxity

KW - invariant estimator

KW - nonparametric estimator

KW - product measure

KW - uniform distribution on a set

UR - https://www.scopus.com/pages/publications/0010625778

U2 - 10.1007/BF00053401

DO - 10.1007/BF00053401

M3 - Article

SN - 0020-3157

VL - 44

SP - 729

EP - 735

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

IS - 4

ER -

Minimax invariant estimator of a continuous distribution function

Abstract

Keywords

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