Minimax estimation of a bounded squared mean

Jianqing Fan; Irène Gijbels

doi:10.1016/0167-7152(92)90111-H

Minimax estimation of a bounded squared mean

Jianqing Fan, Irène Gijbels

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

1 Scopus citations

Abstract

Consider a normal model with unknown mean bounded by a known constant. This paper deals with minimax estimation of the squared mean. We establish an expression for the asymptotic minimax risk. This result is applied in nonparametric estimation of quadratic functionals.

Original language	English (US)
Pages (from-to)	383-390
Number of pages	8
Journal	Statistics and Probability Letters
Volume	13
Issue number	5
DOIs	https://doi.org/10.1016/0167-7152(92)90111-H
State	Published - Apr 7 1992
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Bayes risk
Gaussian white noise model
hardest 1-dimensional subproblems
minimax risk
normal mean
quadratic functionals

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10.1016/0167-7152(92)90111-H

Cite this

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title = "Minimax estimation of a bounded squared mean",

abstract = "Consider a normal model with unknown mean bounded by a known constant. This paper deals with minimax estimation of the squared mean. We establish an expression for the asymptotic minimax risk. This result is applied in nonparametric estimation of quadratic functionals.",

keywords = "Bayes risk, Gaussian white noise model, hardest 1-dimensional subproblems, minimax risk, normal mean, quadratic functionals",

author = "Jianqing Fan and Ir{\`e}ne Gijbels",

year = "1992",

month = apr,

day = "7",

doi = "10.1016/0167-7152(92)90111-H",

language = "English (US)",

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publisher = "Elsevier B.V.",

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T1 - Minimax estimation of a bounded squared mean

AU - Fan, Jianqing

AU - Gijbels, Irène

PY - 1992/4/7

Y1 - 1992/4/7

N2 - Consider a normal model with unknown mean bounded by a known constant. This paper deals with minimax estimation of the squared mean. We establish an expression for the asymptotic minimax risk. This result is applied in nonparametric estimation of quadratic functionals.

AB - Consider a normal model with unknown mean bounded by a known constant. This paper deals with minimax estimation of the squared mean. We establish an expression for the asymptotic minimax risk. This result is applied in nonparametric estimation of quadratic functionals.

KW - Bayes risk

KW - Gaussian white noise model

KW - hardest 1-dimensional subproblems

KW - minimax risk

KW - normal mean

KW - quadratic functionals

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U2 - 10.1016/0167-7152(92)90111-H

DO - 10.1016/0167-7152(92)90111-H

M3 - Article

AN - SCOPUS:44049117341

SN - 0167-7152

VL - 13

SP - 383

EP - 390

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 5

ER -

Minimax estimation of a bounded squared mean

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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