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Kernel regression 2026-10-14

Kernel regression estimates a regression function using localized kernel weights rather than a fixed finite-dimensional functional form. The Nadaraya–Watson estimator is the local-constant version; local polynomial regression improves its local approximation by fitting a polynomial.

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Nadaraya–Watson estimator Created 2026-09-28 Updated 2026-10-14

This local-constant estimator is one particular kernel regression method.

The Nadaraya–Watson estimator is the degree-zero local polynomial estimate

m (x) = \frac{\sum _{i} K (( x _{i} - x ) / h ) Y _{i}}{\sum _{i} K (( x _{i} - x ) / h )} .

At a support boundary it generally has first-order bias because it reproduces constants but not linear functions.

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