We consider the recursive estimation of the probability density function of continuous random variables from a strongly mixing random sample. We revisit here earlier research on this subject by considering a more general class of recursive estimators, including the usual ones. We derive the quadratic mean error of the considered class of estimators. Moreover, we establish a central limit theorem by using Lindeberg’s method resulting in a simplification of the existing assumptions on the sequence of smooth parameters and the mixing coefficient. This is the main contribution of this paper. Finally, the feasibility of the proposed estimator is illustrated throughout an empirical study.

中文翻译：

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时间序列的递归核密度估计

我们考虑从强混合随机样本中递归估计连续随机变量的概率密度函数。我们通过考虑更一般的递归估计器（包括通常的估计器）来重新审视有关该主题的早期研究。我们推导出所考虑的估计量类的二次平均误差。此外，我们通过使用林德伯格方法建立了中心极限定理，从而简化了对平滑参数序列和混合系数的现有假设。这是本文的主要贡献。最后，在整个实证研究中说明了所提出的估计器的可行性。