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==Minimum Mean-Square Estimation (MMSE)== | ==Minimum Mean-Square Estimation (MMSE)== | ||
| − | <math>\hat{y}_{\rm MMSE}(x) \int\limits_{-\infty}^{\infty}\ {y}{f}_{\rm y|x}(Y|X=x)\, dy={E}(Y|X=x)</math> | + | <math>\hat{y}_{\rm MMSE}(x) = \int\limits_{-\infty}^{\infty}\ {y}{f}_{\rm y|x}(Y|X=x)\, dy={E}(Y|X=x)</math> |
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Mean square error : <math>MSE = E[(\theta - \hat \theta(x))^2]</math> | Mean square error : <math>MSE = E[(\theta - \hat \theta(x))^2]</math> | ||
==Linear Minimum Mean-Square Estimation (LMMSE)== | ==Linear Minimum Mean-Square Estimation (LMMSE)== | ||
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| + | <math>\hat{y}_{\rm LMMSE}(x) = E[\theta]+\frac{COV(x,\theta)}{Var(x)}*(x-E[x])</math> | ||
==Hypothesis Testing: ML Rule== | ==Hypothesis Testing: ML Rule== | ||
Revision as of 16:38, 11 December 2008
Contents
Maximum Likelihood Estimation (ML)
Maximum A-Posteriori Estimation (MAP)
Minimum Mean-Square Estimation (MMSE)
$ \hat{y}_{\rm MMSE}(x) = \int\limits_{-\infty}^{\infty}\ {y}{f}_{\rm y|x}(Y|X=x)\, dy={E}(Y|X=x) $
Mean square error : $ MSE = E[(\theta - \hat \theta(x))^2] $
Linear Minimum Mean-Square Estimation (LMMSE)
$ \hat{y}_{\rm LMMSE}(x) = E[\theta]+\frac{COV(x,\theta)}{Var(x)}*(x-E[x]) $
Hypothesis Testing: ML Rule
Type I error
Type II error
Hypothesis Testing: MAP Rule
Overall P(err)
