Uniform convergence rates for nonparametric estimators smoothed by the beta kernel

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Uniform convergence rates for nonparametric estimators smoothed by the beta kernel. / Hirukawa, Masayuki; Murtazashvili, Irina; Prokhorov, Artem.

In: Scandinavian Journal of Statistics, Vol. 49, No. 3, 09.2022, p. 1353-1382.

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

Author

Hirukawa, Masayuki ; Murtazashvili, Irina ; Prokhorov, Artem. / Uniform convergence rates for nonparametric estimators smoothed by the beta kernel. In: Scandinavian Journal of Statistics. 2022 ; Vol. 49, No. 3. pp. 1353-1382.

BibTeX

@article{f4aad7f2ace54738b1d1f57a934b6761,

title = "Uniform convergence rates for nonparametric estimators smoothed by the beta kernel",

abstract = "This paper provides a set of uniform consistency results with rates for nonparametric density and regression estimators smoothed by the beta kernel having support on the unit interval. Weak and strong uniform convergence is explored on the basis of expanding compact sets and general sequences of smoothing parameters. The results in this paper are useful for asymptotic analysis of two-step semiparametric estimation using a first-step kernel estimate as a plug-in. We provide simulations and a real data example illustrating attractive properties of the estimators.",

keywords = "beta kernel, boundary bias, nonparametric density estimation, nonparametric regression estimation, rates of convergence, MULTIPLICATIVE BIAS CORRECTION, DENSITY-ESTIMATION, REGRESSION, MODELS",

author = "Masayuki Hirukawa and Irina Murtazashvili and Artem Prokhorov",

note = "Publisher Copyright: {\textcopyright} 2022 The Board of the Foundation of the Scandinavian Journal of Statistics.",

year = "2022",

month = sep,

doi = "10.1111/sjos.12573",

language = "English",

volume = "49",

pages = "1353--1382",

journal = "Scandinavian Journal of Statistics",

issn = "0303-6898",

publisher = "Wiley-Blackwell",

number = "3",

}

RIS

TY - JOUR

T1 - Uniform convergence rates for nonparametric estimators smoothed by the beta kernel

AU - Hirukawa, Masayuki

AU - Murtazashvili, Irina

AU - Prokhorov, Artem

PY - 2022/9

Y1 - 2022/9

N2 - This paper provides a set of uniform consistency results with rates for nonparametric density and regression estimators smoothed by the beta kernel having support on the unit interval. Weak and strong uniform convergence is explored on the basis of expanding compact sets and general sequences of smoothing parameters. The results in this paper are useful for asymptotic analysis of two-step semiparametric estimation using a first-step kernel estimate as a plug-in. We provide simulations and a real data example illustrating attractive properties of the estimators.

AB - This paper provides a set of uniform consistency results with rates for nonparametric density and regression estimators smoothed by the beta kernel having support on the unit interval. Weak and strong uniform convergence is explored on the basis of expanding compact sets and general sequences of smoothing parameters. The results in this paper are useful for asymptotic analysis of two-step semiparametric estimation using a first-step kernel estimate as a plug-in. We provide simulations and a real data example illustrating attractive properties of the estimators.

KW - beta kernel

KW - boundary bias

KW - nonparametric density estimation

KW - nonparametric regression estimation

KW - rates of convergence

KW - MULTIPLICATIVE BIAS CORRECTION

KW - DENSITY-ESTIMATION

KW - REGRESSION

KW - MODELS

UR - http://www.scopus.com/inward/record.url?scp=85123595554&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/2e1e0a06-1970-3bce-9205-6dc7d6899341/

U2 - 10.1111/sjos.12573

DO - 10.1111/sjos.12573

M3 - Article

AN - SCOPUS:85123595554

VL - 49

SP - 1353

EP - 1382

JO - Scandinavian Journal of Statistics

JF - Scandinavian Journal of Statistics

SN - 0303-6898

IS - 3

ER -

ID: 94060566