Near-Linear Time Local Polynomial Nonparametric Estimation

Nonparametric density and function estimation is an important question in both statistics and machine learning research (Larry, 2006; Tsybakov, 2009; Friedman et al., 2001). Example applications of nonparametric function estimation include smoothing and prediction of econometric trends like loan management, market profit prediction and wheat crop predictions (Györfi et al., 2006). The nonparametric density estimation problem, on the other hand, is useful for exploratory analysis of unlabeled data, and also has applications in other fields such as computer vision (Miller & Chefd'Hotel, 2003) and computational fluid mechanics (Eugeciouglu & Srinivasan, 2000).