What is the difference between MVUE and Umvue?

In statistics a minimum-variance unbiased estimator (MVUE) or uniformly minimum-variance unbiased estimator (UMVUE) is an unbiased estimator that has lower variance than any other unbiased estimator for all possible values of the parameter.

How do you find the uniformly minimum variance of an unbiased estimator?

If there exists an unbiased estimator of ϑ, then ϑ is called an estimable parameter. Definition 3.1. An unbiased estimator T(X) of ϑ is called the uniformly minimum variance unbiased estimator (UMVUE) if and only if Var(T(X)) ≤ Var(U(X)) for any P ∈ P and any other unbiased estimator U(X) of ϑ.

Why we use Cramer Rao inequality?

The Cramér–Rao inequality is important because it states what the best attainable variance is for unbiased estimators. Estimators that actually attain this lower bound are called efficient. It can be shown that maximum likelihood estimators asymptotically reach this lower bound, hence are asymptotically efficient.

What is the use of Cramer Rao lower bound?

The Cramer-Rao Lower Bound (CRLB) gives a lower estimate for the variance of an unbiased estimator. Estimators that are close to the CLRB are more unbiased (i.e. more preferable to use) than estimators further away.

What is the minimum variance portfolio?

Minimum Variance Portfolio is the technical way of representing a low-risk portfolio. It carries low volatility as it correlates to your expected return (you’re not assuming greater risk than is necessary). Obviously, a one line description won’t be enough to satisfy all doubts.

Why minimum variance unbiased estimators are considered efficient estimators?

An efficient estimator is also the minimum variance unbiased estimator (MVUE). This is because an efficient estimator maintains equality on the Cramér–Rao inequality for all parameter values, which means it attains the minimum variance for all parameters (the definition of the MVUE).

Is UMVUE unique?

Generally, an UMVUE is essentially unique. The estimator you provided is not an UMVUE though, indeed it is not even unbiased!! Notice that E[1−X]=1−E[X]=1−p provided that our random variable is a Bernoulli with parameter p. I’d suggest to proceed finding the UMVUE for p(1−p).