Sharp minimaxity and spherical deconvolution for super-smooth error distributions

Peter T. Kim; Ja Yong Koo; Heon Jin Park

doi:10.1016/j.jmva.2003.08.004

Sharp minimaxity and spherical deconvolution for super-smooth error distributions

Peter T. Kim^*
, Ja Yong Koo
, Heon Jin Park

^*Corresponding author for this work

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

12 Citations (Scopus)

Abstract

The spherical deconvolution problem was first proposed by Rooij and Ruymgaart (in: G. Roussas (Ed.), Nonparametric Functional Estimation and Related Topics, Kluwer Academic Publishers, Dordrecht, 1991, pp. 679-690) and subsequently solved in Healy et al. (J. Multivariate Anal. 67 (1998) 1). Kim and Koo (J. Multivariate Anal. 80 (2002) 21) established minimaxity in the L²-rate of convergence. In this paper, we improve upon the latter and establish sharp minimaxity under a super-smooth condition on the error distribution.

Original language	English
Pages (from-to)	384-392
Number of pages	9
Journal	Journal of Multivariate Analysis
Volume	90
Issue number	2
DOIs	https://doi.org/10.1016/j.jmva.2003.08.004
Publication status	Published - 2004 Aug
Externally published	Yes

Keywords

Hellinger distance
Rotational harmonics
Sobolev spaces
Spherical harmonics

ASJC Scopus subject areas

Statistics and Probability
Numerical Analysis
Statistics, Probability and Uncertainty

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10.1016/j.jmva.2003.08.004

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title = "Sharp minimaxity and spherical deconvolution for super-smooth error distributions",

abstract = "The spherical deconvolution problem was first proposed by Rooij and Ruymgaart (in: G. Roussas (Ed.), Nonparametric Functional Estimation and Related Topics, Kluwer Academic Publishers, Dordrecht, 1991, pp. 679-690) and subsequently solved in Healy et al. (J. Multivariate Anal. 67 (1998) 1). Kim and Koo (J. Multivariate Anal. 80 (2002) 21) established minimaxity in the L2-rate of convergence. In this paper, we improve upon the latter and establish sharp minimaxity under a super-smooth condition on the error distribution.",

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author = "Kim, \{Peter T.\} and Koo, \{Ja Yong\} and Park, \{Heon Jin\}",

year = "2004",

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doi = "10.1016/j.jmva.2003.08.004",

language = "English",

volume = "90",

pages = "384--392",

journal = "Journal of Multivariate Analysis",

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AU - Kim, Peter T.

AU - Koo, Ja Yong

AU - Park, Heon Jin

PY - 2004/8

Y1 - 2004/8

N2 - The spherical deconvolution problem was first proposed by Rooij and Ruymgaart (in: G. Roussas (Ed.), Nonparametric Functional Estimation and Related Topics, Kluwer Academic Publishers, Dordrecht, 1991, pp. 679-690) and subsequently solved in Healy et al. (J. Multivariate Anal. 67 (1998) 1). Kim and Koo (J. Multivariate Anal. 80 (2002) 21) established minimaxity in the L2-rate of convergence. In this paper, we improve upon the latter and establish sharp minimaxity under a super-smooth condition on the error distribution.

AB - The spherical deconvolution problem was first proposed by Rooij and Ruymgaart (in: G. Roussas (Ed.), Nonparametric Functional Estimation and Related Topics, Kluwer Academic Publishers, Dordrecht, 1991, pp. 679-690) and subsequently solved in Healy et al. (J. Multivariate Anal. 67 (1998) 1). Kim and Koo (J. Multivariate Anal. 80 (2002) 21) established minimaxity in the L2-rate of convergence. In this paper, we improve upon the latter and establish sharp minimaxity under a super-smooth condition on the error distribution.

KW - Hellinger distance

KW - Rotational harmonics

KW - Sobolev spaces

KW - Spherical harmonics

UR - https://www.scopus.com/pages/publications/3042693283

U2 - 10.1016/j.jmva.2003.08.004

DO - 10.1016/j.jmva.2003.08.004

M3 - Article

AN - SCOPUS:3042693283

SN - 0047-259X

VL - 90

SP - 384

EP - 392

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

IS - 2

ER -

Sharp minimaxity and spherical deconvolution for super-smooth error distributions

Abstract

Keywords

ASJC Scopus subject areas

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