Kernel estimators of density function of directional data
Journal of Multivariate Analysis - Memorial volume dedicated to P. R. Krishnaiah
Bootstrapping the mean integrated squared error
Journal of Multivariate Analysis
A comparative study of several smoothing methods in density estimation
Computational Statistics & Data Analysis
Estimation of densities and derivatives of densities with directional data
Journal of Multivariate Analysis
Automatic bandwidth selection for circular density estimation
Computational Statistics & Data Analysis
Kernel Density Estimation on Riemannian Manifolds: Asymptotic Results
Journal of Mathematical Imaging and Vision
A plug-in rule for bandwidth selection in circular density estimation
Computational Statistics & Data Analysis
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A nonparametric kernel density estimator for directional-linear data is introduced. The proposal is based on a product kernel accounting for the different nature of both (directional and linear) components of the random vector. Expressions for the bias, variance, and mean integrated square error (MISE) are derived, jointly with an asymptotic normality result for the proposed estimator. For some particular distributions, an explicit formula for the MISE is obtained and compared with its asymptotic version, both for directional and directional-linear kernel density estimators. In this same setting, a closed expression for the bootstrap MISE is also derived.