Solving a Linear Mean Square Estimation the Easy Way

1. What is linear mean square estimation?
2. How do you find the minimum mean square error?
3. What is linear estimate?

What is linear mean square estimation?

Linear 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.

How do you find the minimum mean square 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 linear estimate?

From Encyclopedia of Mathematics. A linear function of observable random variables, used (when the actual values of the observed variables are substituted into it) as an approximate value (estimate) of an unknown parameter of the stochastic model under analysis (see Statistical estimator).