Exact asymptotic limit for kernel estimation of regression level sets

Dau Hai Dang (1) , Thomas Laloë (1) , Rémi Servien (2)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 InTheRes - Innovations Thérapeutiques et Résistances

The asymptotic behavior of a plug-in kernel estimator of the regression level sets is studied. The exact asymtotic rate in terms of the symmetric difference is derived for a given level. Then, we exhibit the exact asymptotic rate when the level corresponds to a fixed probability and is therefore unknown.

Domaines: Théorie [stat.TH]

Dau Hai Dang, Thomas Laloë, Rémi Servien. Exact asymptotic limit for kernel estimation of regression level sets. Statistics and Probability Letters, 2020, 161 (108721), ⟨10.1016/j.spl.2020.108721⟩. ⟨hal-02073071v2⟩