## Electronic Journal of Statistics

### Exact risk improvement of bandwidth selectors for kernel density estimation with directional data

Eduardo García–Portugués

#### Abstract

New bandwidth selectors for kernel density estimation with directional data are presented in this work. These selectors are based on asymptotic and exact error expressions for the kernel density estimator combined with mixtures of von Mises distributions. The performance of the proposed selectors is investigated in a simulation study and compared with other existing rules for a large variety of directional scenarios, sample sizes and dimensions. The selector based on the exact error expression turns out to have the best behaviour of the studied selectors for almost all the situations. This selector is illustrated with real data for the circular and spherical cases.

#### Article information

Source
Electron. J. Statist., Volume 7 (2013), 1655-1685.

Dates
First available in Project Euclid: 19 June 2013

https://projecteuclid.org/euclid.ejs/1371649230

Digital Object Identifier
doi:10.1214/13-EJS821

Mathematical Reviews number (MathSciNet)
MR3070874

Zentralblatt MATH identifier
1327.62241

Subjects
Primary: 62G07: Density estimation

#### Citation

García–Portugués, Eduardo. Exact risk improvement of bandwidth selectors for kernel density estimation with directional data. Electron. J. Statist. 7 (2013), 1655--1685. doi:10.1214/13-EJS821. https://projecteuclid.org/euclid.ejs/1371649230

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