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Goodness‐of‐fit Test for Directional Data
Author(s) -
Boente Graciela,
Rodriguez Daniela,
Manteiga Wenceslao González
Publication year - 2014
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12020
Subject(s) - mathematics , test statistic , statistics , estimator , goodness of fit , kolmogorov–smirnov test , statistical hypothesis testing , null distribution , null hypothesis , parametric statistics , one and two tailed tests
In this paper, we study the problem of testing the hypothesis on 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 distances between a non‐parametric 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 hypothesis and 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 by analysing a real data set based on wind direction measurements.