# Central limit theorems for directional and linear random variables with applications

arXiv: https://arxiv.org/abs/1402.6836 · HTML: https://mlsanity.com/paper/1402.6836/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2014.

## Built on by (most cited first, 2 of 2)

- [Reproducing Kernels and New Approaches in Compositional Data Analysis](https://mlsanity.com/paper/2205.01158/) (2022)
- [Mode and Ridge Estimation in Euclidean and Directional Product Spaces: A Mean Shift Approach](https://mlsanity.com/paper/2110.08505/) (2021)

## Abstract (arXiv)

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 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 sciences.