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| Both sides previous revision Previous revision Next revision | Previous revision | ||
| kb:mmse_estimator [2021-05-24 02:14] – jaeyoung | kb:mmse_estimator [2024-04-30 04:03] (current) – external edit 127.0.0.1 | ||
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| The resulting MSE from a linear MMSE estimator is: | The resulting MSE from a linear MMSE estimator is: | ||
| - | $$ E[(\tilde{Y} - a\tilde{X})^2] = \sigma_Y^2 (1 - \rho^2) = \sigma_Y^2 \left[ 1 - (\frac{\sigma_{XY}}{\sigma_X \sigma_Y})^2 \right] $$ | + | $$ E[(\tilde{Y} - a\tilde{X})^2] = \sigma_Y^2 (1 - \rho^2) = \sigma_Y^2 \left[ 1 - \left( \frac{\sigma_{XY}}{\sigma_X \sigma_Y} |
| ==== Orthogonalities ==== | ==== Orthogonalities ==== | ||