García Portugués, EduardoCrujeiras Casais, Rosa MaríaGonzález Manteiga, Wenceslao2019-04-092019-04-092015García-Portugués, E., Crujeiras, R. M. & González Manteiga, W. (2015). Central limit theorems for directional and linear random variables with applications. Statistica Sinica, 25, 1207-1229. doi: 10.5705/ss.2014.1531017-0405http://hdl.handle.net/10347/18562A central limit theorem for the integrated squared error of the directional-linear kernel density estimator is established. The result enables the construction and analysis of two testing procedures based on squared loss: a nonparametric independence test for directional and linear random variables and a goodness-of-fit test for parametric families of directional-linear densities. Limit distributions for both test statistics, and a consistent bootstrap strategy for the goodness-of-fit test, are developed for the directional-linear case and adapted to the directional-directional setting. Finite sample performance for the goodness-of-fit test is illustrated in a simulation study. This test is also applied to datasets from biology and environmental scienceseng© 2007 Academia Sinica, Institute of Statistical ScienceDirectional dataGoodness-of-fitIndependence testKernel density estimationLimit distributionjournal article10.5705/ss.2014.1531996-8507open access