Howtosignalprocessing
- How do I minimize MSE?
- What is the value of C that minimizes the mean square error?
- Can there exist an estimator with the smaller MSE than minimal least squares?
- How do you calculate MMSE estimator?
How do I minimize MSE?
You can use Excel's Solver to minimize mean squared error. Set the solver to minimize the MSE cell, by changing the alpha and beta cells, subject to alpha and beta between 0 and 1. Excel's Data/Table command can also be useful to see how different input values affect the MSE.
What is the value of C that minimizes the mean square error?
(b) Find the value of c which minimizes the mean square error. This is the risk when we take the loss function to be (T − θ)2. Note that we can factor out a θ2, which implies that the minimizing c will not depend on θ. Minimize this as a function of c and you should get c = 3/2.
Can there exist an estimator with the smaller MSE than minimal least squares?
Although there have been proposed biased estimators which are shown to have smaller MSE than the ordinary least squares estimator, our construction is based on the minimization of relative MSE directly. The performance of the proposed methods is illustrated by a simulation study and a real data example.
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.
