Goodness‐of‐fit Test for Directional Data. (29th May 2013)

• Record Type: Journal Article
• Authors: Boente, Graciela; Rodriguez, Daniela; Manteiga, Wenceslao González
• Is Part Of: Scandinavian journal of statistics. Volume 41:Number 1(2014:Mar.)
• Page Start: 259
• Page End: 275
• Publication Date: 2013-05-29
• Subjects: Statistics -- Periodicals; 310
• DOI: 10.1111/sjos.12020
• Languages: English
• ISSNs: 0303-6898

Abstract

<abstract abstract-type="main" id="sjos12020-abs-0001"> <title>ABSTRACT</title> <p id="sjos12020-para-0002">In this paper, we study the problem of testing the hypothesis on whether the density <italic>f</italic> of a random variable on a sphere belongs to a given parametric class of densities. We propose two test statistics based on the <italic>L</italic>² and <italic>L</italic>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 <italic>L</italic>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.</p> </abstract>