Quadratic errors for nonparametric estimates under dependence

We investigate nonparametric curve estimation (including density, distribution, hazard, conditional density, and regression functions estimation) by kernel methods when the observed data satisfy a strong mixing condition. In a first attempt we show asymptotic equivalence of average square errors, integrated square errors, and mean integrated square errors. These results are extensions to dependent data of several works, in particular of those by Marron and Härdle (1986, J. Multivariate Anal. 20 91-113). Then we give precise asymptotic evaluations of these errors.