Kernel for nonparametric regression

A nonnegative regression kernel supplies weights $K((x_i-x)/h)$ in a local weighted least squares fit. Unlike a probability density function, its integral need not equal one, because rescaling every weight does not change the fitted coefficients.

A smoothing bandwidth determines the spatial scale over which a regression kernel averages data. Larger values reduce variance and may increase the bias of an estimator.

The uniform smoothing kernel assigns equal weight inside the window $[x-h,x+h]$ and zero weight outside. Its Nadaraya–Watson estimator is the average of observations in that window.