Nonparametric estimation of the spectral density of amplitude-modulated time series with missing observations

Efromovich, Sam

doi:10.1016/j.spl.2014.06.013

Cited by 2 publications

(3 citation statements)

References 14 publications

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“…This is an attractive example of using the sharp minimax estimation theory. More results can be found in Efromovich [8,11,14] .…”

Section: Spectral Density Estimation With Missing Datamentioning

confidence: 95%

“…Further, there exists a data-driven estimator that attains this lower bound [8,11] . Now let us consider the following puzzling question.…”

Section: Spectral Density Estimation With Missing Datamentioning

confidence: 99%

“…It is a great honour to present the invited keynote address at the Ninth International Triennial Calcutta Symposium on Probability and Statistics, and I am grateful to the organizers for the opportunity to talk about my recent results [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] in nonparametric curve estimation. The article is based on the address, and it covers a wide variety of topics ranging from the minimax superefficiency and sequential estimation for direct data to missing/modified data and wavelet applications in Big Data.…”

Section: Introductionmentioning

confidence: 99%

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Missing, Modified, and Large-p-small-nData in Nonparametric Curve Estimation

Efromovich

2017

Calcutta Statistical Association Bulletin

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Nonparametric curve estimation, which makes no assumptions about shape of estimated functions, is one of the main pillars of the modern statistical science. It is used when no adequate parametric or semi-parametric model is available. Asymptotic results on adaptive estimation of nonparametric curves, under both traditional and shrinking minimaxes, are presented. The latter approach allows us to explain the phenomenon of superefficiency when a function can be estimated with a rate faster than the minimax one. Resent results on sequential nonparametric estimation, which yields an assigned risk with minimal average stopping time, are also presented. Then it is explained how the theory can be used in practically important cases of missing data, modified data in survival analysis, and Big Data. Wavelet applications in the analysis of microarrays and fMRI illustrate feasibility of the proposed nonparametric estimation.

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“…This is an attractive example of using the sharp minimax estimation theory. More results can be found in Efromovich [8,11,14] .…”

Section: Spectral Density Estimation With Missing Datamentioning

confidence: 95%

“…Further, there exists a data-driven estimator that attains this lower bound [8,11] . Now let us consider the following puzzling question.…”

Section: Spectral Density Estimation With Missing Datamentioning

confidence: 99%