Goodness-of-fit test for directional data

BOENTE, GRACIELA; GONZALEZ-MANTEIGA, WENCESLAO; RODRIGUEZ, DANIELA

SCANDINAVIAN JOURNAL OF STATISTICS

WILEY-BLACKWELL PUBLISHING, INC

Lugar: Londres; Año: 2014 vol. 41 p. 259 - 275

0303-6898

In this paper, we study the problem of testing the hypothesis whether the density $f$ of a random variable on a sphere belongs to a given parametric class of densities. We propose two test statistics based on the $L^2$ and $L^1$ distance between a nonparametric density estimator adapted to circular data and a smoothed version of the specified density. The asymptotic distribution of the $L^2$ test statistic is provided under the null and under contiguous alternatives. We also consider a bootstrap method to approximate the distribution of both test statistics. Through a simulation study, we explore the moderate sample performance of the proposed tests under the null hypothesis and under different alternatives. Finally, the procedure is illustrated analysing a real data set based on wind directions measurements.