Kernel smoother

A kernel smoother is a statistical technique to estimate a real valued function f : R p → R {displaystyle f:mathbb {R} ^{p} o mathbb {R} } as the weighted average of neighboring observed data. The weight is defined by the kernel, such that closer points are given higher weights. The estimated function is smooth, and the level of smoothness is set by a single parameter. A kernel smoother is a statistical technique to estimate a real valued function f : R p → R {displaystyle f:mathbb {R} ^{p} o mathbb {R} } as the weighted average of neighboring observed data. The weight is defined by the kernel, such that closer points are given higher weights. The estimated function is smooth, and the level of smoothness is set by a single parameter. This technique is most appropriate when the dimension of the predictor is low (p < 3), for example for data visualization. Let K h λ ( X 0 , X ) {displaystyle K_{h_{lambda }}(X_{0},X)} be a kernel defined by