Central limit theorems for directional and linear random variables with applications

@article{GarciaPortugues2014CentralLT,
  title={Central limit theorems for directional and linear random variables with applications},
  author={Eduardo Garc'ia-Portugu'es and Rosa M. Crujeiras and Wenceslao Gonz'alez-Manteiga},
  journal={arXiv: Methodology},
  year={2014}
}
A 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… 

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