The paper considers nonparametric kernel density/regression estimation from a stochastic optimization point of view. The estimation problem is represented through a family of stochastic optimization problems. Recursive constrained estimators are obtained by application of stochastic (quasi)gradient methods to these problems, classical kernel estimates are derived as particular cases. Accuracy and rate of convergence of the obtained estimates are established, and asymptotically optimal estimation procedure parameters are found. The case of moving density/regression is particularly studied.

翻译：本文从随机优化的角度研究非参数核密度/回归估计问题。通过构建一族随机优化问题来表征估计任务，并应用随机（拟）梯度方法求解这些问题，从而得到约束递归估计器，经典核估计可作为其特例导出。文中建立了所得估计量的精度与收敛速率，并确定了渐近最优的估计过程参数。特别研究了动态密度/回归情形下的估计问题。