 Leave-one-out residual identity for a linear smoother

ID: leave-one-out-residual-identity-for-a-linear-smoother

Y = H Y

, its residual after fitting without observation

i

Y_{i} - Y_{- i, i} = \frac{Y _{i} - Y _{i}}{1 - H _{ii}} .

The identity follows from a block matrix inverse or a rank-one inverse update.

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