Semi-parametric second-order efficient estimation of the period of a signal

I.S.J. Castillo

doi:10.3150/07-BEJ5077

Semi-parametric second-order efficient estimation of the period of a signal

I.S.J. Castillo

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

This paper is concerned with the estimation of the period of an unknown periodic function in Gaussian white noise. A class of estimators of the period is constructed by means of a penalized maximum likelihood method. A second-order asymptotic expansion of the risk of these estimators is obtained. Moreover, the minimax problem for the second-order term is studied and an estimator of the preceding class is shown to be second order efficient. © 2007 ISI/BS.

Original language	English
Pages (from-to)	910-932
Journal	Bernoulli: A Journal of Mathematical Statistics and Probability
Volume	13
Issue number	4
DOIs	https://doi.org/10.3150/07-BEJ5077
Publication status	Published - 2007

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MR2364219

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10.3150/07-BEJ5077

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title = "Semi-parametric second-order efficient estimation of the period of a signal",

abstract = "This paper is concerned with the estimation of the period of an unknown periodic function in Gaussian white noise. A class of estimators of the period is constructed by means of a penalized maximum likelihood method. A second-order asymptotic expansion of the risk of these estimators is obtained. Moreover, the minimax problem for the second-order term is studied and an estimator of the preceding class is shown to be second order efficient. {\textcopyright} 2007 ISI/BS.",

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AB - This paper is concerned with the estimation of the period of an unknown periodic function in Gaussian white noise. A class of estimators of the period is constructed by means of a penalized maximum likelihood method. A second-order asymptotic expansion of the risk of these estimators is obtained. Moreover, the minimax problem for the second-order term is studied and an estimator of the preceding class is shown to be second order efficient. © 2007 ISI/BS.

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DO - 10.3150/07-BEJ5077

M3 - Article

SN - 1350-7265

VL - 13

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EP - 932

JO - Bernoulli: A Journal of Mathematical Statistics and Probability

JF - Bernoulli: A Journal of Mathematical Statistics and Probability

IS - 4

ER -

Semi-parametric second-order efficient estimation of the period of a signal

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