The Annals of Statistics

Estimation of the Spectral Parameters of a Stationary Point Process

Pham Dinh Tuan

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Abstract

This paper considers the two approaches for estimating the parameters specifying the spectral density of the counting process of a stationary point process, namely the frequency domain and the time domain approaches. The relation between the two is clarified; consistency and asymptotic normality of the estimates are established. Finally the special case of a rational spectral density is considered in some detail.

Article information

Source
Ann. Statist., Volume 9, Number 3 (1981), 615-627.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345465

Digital Object Identifier
doi:10.1214/aos/1176345465

Mathematical Reviews number (MathSciNet)
MR615437

Zentralblatt MATH identifier
0475.62074

JSTOR
links.jstor.org

Subjects
Primary: 60G10: Stationary processes
Secondary: 62F10: Point estimation 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Keywords
Cumulant least square estimation maximum likelihood estimation periodogram point process spectral density

Citation

Tuan, Pham Dinh. Estimation of the Spectral Parameters of a Stationary Point Process. Ann. Statist. 9 (1981), no. 3, 615--627. doi:10.1214/aos/1176345465. https://projecteuclid.org/euclid.aos/1176345465


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