Derivation of the LMMSE (Linear Minimum Mean Squared Error) Estimate and the MMSE Under Gaussian Prior

1. How do you calculate MMSE estimator?
2. Is MMSE the same as MSE?
3. How do you find the minimum mean squared error?
4. What is MMSE estimation?

How do you calculate MMSE estimator?

The linear MMSE estimator of the random variable X, given that we have observed Y, is given by ˆXL=Cov(X,Y)Var(Y)(Y−EY)+EX=ρσXσY(Y−EY)+EX. The estimation error, defined as ˜X=X−ˆXL, satisfies the orthogonality principle: E[˜X]=0,Cov(˜X,Y)=E[˜XY]=0.

Is MMSE the same as MSE?

The MSE is not to be confused with the Mini-Mental State Examination (MMSE), which is a brief neuropsychological screening test for cognitive impairment and suspected dementia. However, the MMSE can be used for more detailed testing in the cognitive section of this MSE.

How do you find the minimum mean squared error?

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.

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.