Weights explain the estimate
At each query, Gaussian distance weights are normalized to sum to one. The estimate is their weighted average.
Let nearby points speak louder.
Fit without choosing a fixed equation. Then make the flexibility answer to leave-one-out error, point weights, and visible residuals.
Observed data and tuning grid
wᵢ(x)=exp[-0.5((x-xᵢ)/h)²]
ŷ(x)=Σwᵢyᵢ / Σwᵢ
CV(h)=mean[(yᵢ-ŷ₋ᵢ(xᵢ))²]
AWAITING FITGAUSSIAN NADARAYA-WATSON
BEST BANDWIDTH—
LOOCV MSE—
ŷ AT QUERY—
Run the fit to inspect dominant normalized weights.
Bandwidth is the argument.
Small h listens locally and can chase noise. Large h pools broadly and can erase structure. Cross-validation makes that tradeoff measurable.
Leave one point out
Each observed y is predicted without using itself. Mean squared error compares candidate bandwidths on equal terms.
Flexible is not causal
The red curve estimates association in this sample. It does not provide confidence intervals, extrapolation guarantees, or causal effects.