Howtosignalprocessing
What is MMSE estimation?
In statistics and signal processing, a minimum mean square error (MMSE) estimator is an estimation method which minimizes the mean square error (MSE), which is a common measure of estimator quality, of the fitted values of a dependent variable.
How is MMSE calculated?
The MSE of the linear MMSE is given by E[(X−XL)2]=E[˜X2]=(1−ρ2)Var(X).
How do you calculate minimum MSE?
That is why it is called the minimum mean squared error (MMSE) estimate. h(a)=E[(X−a)2]=EX2−2aEX+a2. This is a quadratic function of a, and we can find the minimizing value of a by differentiation: h′(a)=−2EX+2a. Therefore, we conclude the minimizing value of a is a=EX.
