kb:mmse_estimator

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kb:mmse_estimator [2021-05-24 02:13] – [Resulting MSE] jaeyoungkb: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:
  
-$$ E[(\tilde{Y} - a\tilde{X})^2] = \sigma_Y^2 (1 - \rho^2) = \sigma_Y^2 [1 - (\frac{\sigma_{XY}}{\sigma_X \sigma_Y})^2] $$+$$ E[(\tilde{Y} - a\tilde{X})^2] = \sigma_Y^2 (1 - \rho^2) = \sigma_Y^2 \left[ 1 - \left( \frac{\sigma_{XY}}{\sigma_X \sigma_Y} \right)^2 \right] $$
  
 ==== Orthogonalities ==== ==== Orthogonalities ====
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