= Local linear regression
{title2=$\widehat f(x)=\widehat a_x$}
Local linear regression fits $a+b(X_i-x)$ to responses near each target $x$ by <weighted least squares>, then returns the fitted intercept. With weights $w_i=K((X_i-x)/h)$, put $S_k=\sum_iw_i(X_i-x)^k$ and $T_k=\sum_iw_i(X_i-x)^kY_i$. If $S_0S_2-S_1^2>0$, then $\widehat f(x)=(S_2T_0-S_1T_1)/(S_0S_2-S_1^2)$. Its <polynomial reproduction property of local polynomial regression> reproduces affine functions, reducing boundary bias relative to a local constant fit.
Back to article page
