statsmodels.nonparametric.kernel_regression.KernelReg.cv_loo¶

KernelReg.cv_loo(bw, func)[source]¶

The cross-validation function with leave-one-out estimator.

Parameters:¶

bwarray_like

Vector of bandwidth values.

funccallable function

Returns the estimator of g(x). Can be either _est_loc_constant (local constant) or _est_loc_linear (local_linear).

Returns:¶

Lfloat

The value of the CV function.

Notes

Calculates the cross-validation least-squares function. This function is minimized by compute_bw to calculate the optimal value of bw.

For details see p.35 in [2]

\[CV(h)=n^{-1}\sum_{i=1}^{n}(Y_{i}-g_{-i}(X_{i}))^{2}\]

where \(g_{-i}(X_{i})\) is the leave-one-out estimator of g(X) and \(h\) is the vector of bandwidths