Monotone spectral density estimation

Dragi Anevski; Philippe Soulier

doi:10.1214/10-AOS804

Monotone spectral density estimation

Dragi Anevski, Philippe Soulier

Mathematical Statistics

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

Abstract

We propose two estimators of a monotone spectral density, that are based on the periodogram. These are the isotonic regression of the periodogram and the isotonic regression of the log-periodogram. We derive pointwise limit distribution results for the proposed estimators for short memory linear processes and long memory Gaussian processes and also that the estimators are rate optimal.

Original language	English
Pages (from-to)	418-438
Journal	Annals of Statistics
Volume	39
DOIs	https://doi.org/10.1214/10-AOS804
Publication status	Published - 2011

Subject classification (UKÄ)

Probability Theory and Statistics

Free keywords

Limit distributions
spectral density estimation
monotone
long-range dependence
Gaussian process
linear process

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10.1214/10-AOS804

http://arxiv.org/pdf/0901.3471

Cite this

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title = "Monotone spectral density estimation",

abstract = "We propose two estimators of a monotone spectral density, that are based on the periodogram. These are the isotonic regression of the periodogram and the isotonic regression of the log-periodogram. We derive pointwise limit distribution results for the proposed estimators for short memory linear processes and long memory Gaussian processes and also that the estimators are rate optimal.",

keywords = "Limit distributions, spectral density estimation, monotone, long-range dependence, Gaussian process, linear process",

author = "Dragi Anevski and Philippe Soulier",

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language = "English",

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T1 - Monotone spectral density estimation

AU - Anevski, Dragi

AU - Soulier, Philippe

PY - 2011

Y1 - 2011

N2 - We propose two estimators of a monotone spectral density, that are based on the periodogram. These are the isotonic regression of the periodogram and the isotonic regression of the log-periodogram. We derive pointwise limit distribution results for the proposed estimators for short memory linear processes and long memory Gaussian processes and also that the estimators are rate optimal.

AB - We propose two estimators of a monotone spectral density, that are based on the periodogram. These are the isotonic regression of the periodogram and the isotonic regression of the log-periodogram. We derive pointwise limit distribution results for the proposed estimators for short memory linear processes and long memory Gaussian processes and also that the estimators are rate optimal.

KW - Limit distributions

KW - spectral density estimation

KW - monotone

KW - long-range dependence

KW - Gaussian process

KW - linear process

U2 - 10.1214/10-AOS804

DO - 10.1214/10-AOS804

M3 - Article

SN - 0090-5364

VL - 39

SP - 418

EP - 438

JO - Annals of Statistics

JF - Annals of Statistics

ER -

Monotone spectral density estimation

Abstract

Subject classification (UKÄ)

Free keywords

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Cite this