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| + | ==Maximum Likelihood Estimation (ML)== | ||
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| + | ==Maximum A-Posteriori Estimation (MAP)== | ||
| + | |||
| + | ==Minimum Mean-Square Estimation (MMSE)== | ||
| + | |||
<math>{y}_{\rm MMSE}(x) \int\limits_{-inf}^{inf}\ {y}{f}_{\rm y|x}(Y|X=x)\, dy={E}(Y|X=x)</math> | <math>{y}_{\rm MMSE}(x) \int\limits_{-inf}^{inf}\ {y}{f}_{\rm y|x}(Y|X=x)\, dy={E}(Y|X=x)</math> | ||
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Mean square estimate : <math>MSE = E[(\theta - \hat \theta(x))^2] | Mean square estimate : <math>MSE = E[(\theta - \hat \theta(x))^2] | ||
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| + | ==Linear Minimum Mean-Square Estimation (LMMSE)== | ||
| + | |||
| + | ==Hypothesis Testing: ML Rule== | ||
| + | |||
| + | Type I error | ||
| + | |||
| + | Type II error | ||
| + | |||
| + | ==Hypothesis Testing: MAP Rule== | ||
| + | |||
| + | Overall P(err) | ||
Revision as of 16:31, 11 December 2008
Maximum Likelihood Estimation (ML)
Maximum A-Posteriori Estimation (MAP)
Minimum Mean-Square Estimation (MMSE)
$ {y}_{\rm MMSE}(x) \int\limits_{-inf}^{inf}\ {y}{f}_{\rm y|x}(Y|X=x)\, dy={E}(Y|X=x) $
$ {y}_{\rm LMMSE}(x)=E[\theta]+\frac{COV(x,\theta)}{Var(x)}*(x-E[x]) $
Mean square estimate : $ MSE = E[(\theta - \hat \theta(x))^2] ==Linear Minimum Mean-Square Estimation (LMMSE)== ==Hypothesis Testing: ML Rule== Type I error Type II error ==Hypothesis Testing: MAP Rule== Overall P(err) $
