Nadaraya–Watson Kernel Regression

Definition

Nadaraya–Watson kernel regression is a Kernel Regression with the sum of the weights is $1$. The Nadaraya–Watson kernel regression estimator is defined as ${\hat{f}}_{\lambda }(x)=\frac{{\sum }_{j=1}^{n}K(\frac{x-X_i}{\lambda })Y_i}{{\sum }_{j=1}^{n}K(\frac{x-X_i}{\lambda })}$ where $K\text{s.t.}{\int }_{-\infty }^{\infty }K(t)dt=1,{\int }_{-\infty }^{\infty }{K}^2(t)dt<\infty$ is the kernel, and $\lambda$ is a smoothing parameter

Facts

Nadaraya–Watson kernel regression estimator is the same as Local Polynomial Regression with $p=0$