Joint behaviour of semirecursive kernel estimators of the location and of the size of the mode of a probability density function

摘要

Let $\theta$ and $\mu$ denote the location and the size of the mode of aprobability density. We study the joint convergence rates of semirecursivekernel estimators of $\theta$ and $\mu$. We show how the estimation of the sizeof the mode allows to measure the relevance of the estimation of its location.We also enlighten that, beyond their computational advantage on nonrecursiveestimators, the semirecursive estimators are preferable to use for theconstruction on confidence regions.