This paper is devoted to the estimation of partial derivatives of multivariate density functions. In this regard, nonparametric linear wavelet-based estimators are introduced, showing their attractive properties from the theoretical point of view. In particular, we prove the strong uniform consistency properties of these estimators, over compact subsets of ${\mathbb{R}}^d$, with the determination of the corresponding convergence rates. Then, we establish the asymptotic normality of these estimators. As a main contribution, we relax some standard dependence conditions; our results hold under a weak dependence condition allowing the consideration of mixing, association, Gaussian sequences and Bernoulli shifts.

本文致力于估计多元密度函数的偏导数。在这方面，引入了基于非参数线性小波的估计器，从理论的角度展示了它们的吸引人的特性。特别是，我们证明了这些估计量在紧凑子集上的强一致一致性属性${\mathbb{电阻}}^d$，确定相应的收敛速度。然后，我们建立这些估计量的渐近正态性。作为主要贡献，我们放宽了一些标准的依赖条件；我们的结果在允许考虑混合、关联、高斯序列和伯努利位移的弱依赖条件下成立。