MSE of an estimator

In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value.

1. How do you calculate MSE of an estimator?
2. Why is MSE an unbiased estimator?
3. What is the MSE and MMSE estimator?
4. What is a good MSE for prediction?

How do you calculate MSE of an estimator?

Let ˆX=g(Y) be an estimator of the random variable X, given that we have observed the random variable Y. The mean squared error (MSE) of this estimator is defined as E[(X−ˆX)2]=E[(X−g(Y))2].

Why is MSE an unbiased estimator?

An estimator whose bias is identically equal to 0 is called unbiased estimator and satisfies E(ˆθ) = θ for all θ. Thus, MSE has two components, one measures the variability of the estimator (precision) and the other measures the its bias (accuracy).

What is the MSE and MMSE estimator?

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.

What is a good MSE for prediction?

There is no correct value for MSE. Simply put, the lower the value the better and 0 means the model is perfect. Since there is no correct answer, the MSE's basic value is in selecting one prediction model over another. Similarly, there is also no correct answer as to what R2 should be.