Question

Do unbiased estimators always have lower mean square error (MSE)? Why or why not?

Answer 1

.The MSE is the second minute (about the inception) of the mistake, and in this way fuses both the fluctuation of the estimator (how broadly spread the assessments are starting with one information test then onto the next) and its inclination (how far away the normal evaluated esteem is from reality).

.For an unbaised estimator, the MSE is the change of the estimator. Like the difference, MSE has the same  units of estimation from the square of the amount being evaluated. In a similarity to standard deviation, taking the square base of MSE yields the root-mean-square blunder or root-mean-square deviation (RMSE or RMSD), which has same  units from the amount being assessed; for an impartial estimator, the RMSE is the square base of the fluctuation, known as the standard error.

.A measurement is said to be unbiased estimate  of a given parameter when the mean of the inspecting circulation of that measurement can be appeared to be equivalent to the parameter being evaluated. For instance, the mean of an example is a fair gauge of the mean of the populace from which the example was drawn.

Therefore yes,the unbiased estimators always have lower mean square error(MSE).