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==Minimum Mean-Square Estimation (MMSE)== | ==Minimum Mean-Square Estimation (MMSE)== | ||
| − | <math>{y}_{\rm MMSE}(x) \int\limits_{- | + | <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>{y}_{\rm LMMSE}(x)=E[\theta]+\frac{COV(x,\theta)}{Var(x)}*(x-E[x])</math> | + | <math>\hat{y}_{\rm LMMSE}(x)=E[\theta]+\frac{COV(x,\theta)}{Var(x)}*(x-E[x])</math> |
Revision as of 15:37, 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) $
$ \hat{y}_{\rm LMMSE}(x)=E[\theta]+\frac{COV(x,\theta)}{Var(x)}*(x-E[x]) $
Mean square error : $ 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)
