## Electronic Journal of Statistics

### Brillinger mixing of determinantal point processes and statistical applications

#### Abstract

Stationary determinantal point processes are proved to be Brillinger mixing. This property is an important step towards asymptotic statistics for these processes. As an important example, a central limit theorem for a wide class of functionals of determinantal point processes is established. This result yields in particular the asymptotic normality of the estimator of the intensity of a stationary determinantal point process and of the kernel estimator of its pair correlation.

#### Article information

Source
Electron. J. Statist., Volume 10, Number 1 (2016), 582-607.

Dates
First available in Project Euclid: 4 March 2016

https://projecteuclid.org/euclid.ejs/1457123507

Digital Object Identifier
doi:10.1214/16-EJS1116

Mathematical Reviews number (MathSciNet)
MR3471989

Zentralblatt MATH identifier
06554158

#### Citation

Biscio, Christophe A. N.; Lavancier, Frédéric. Brillinger mixing of determinantal point processes and statistical applications. Electron. J. Statist. 10 (2016), no. 1, 582--607. doi:10.1214/16-EJS1116. https://projecteuclid.org/euclid.ejs/1457123507

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