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# What is the best linear unbiased estimator?

## What is the best linear unbiased estimator?

Under assumptions V and VI, the OLS estimators are the best linear unbiased estimators (they are best in the sense of having minimum variance among all linear unbiased estimators), regardless of whether the ɛi are normally distributed or not (Gauss–Markov theorem).

### How do you prove OLS estimator is unbiased?

In order to prove that OLS in matrix form is unbiased, we want to show that the expected value of ˆβ is equal to the population coefficient of β. First, we must find what ˆβ is. Then if we want to derive OLS we must find the beta value that minimizes the squared residuals (e).

What is best linear unbiased estimator econometrics?

When the data are generated according to the classical econometric box model, ordinary least squares is the best estimator in the class of linear, unbiased estimators – best, that is, according to the criterion of finding the estimator with the minimum variance for a given sample size.

Will OLS still be the best linear unbiased estimator?

If the estimator is unbiased but doesn’t have the least variance – it’s not the best! If the estimator has the least variance but is biased – it’s again not the best! If the estimator is both unbiased and has the least variance – it’s the best estimator.

## What does best mean in blue?

Best Linear Unbiased Estimates. Definition: The Best Linear Unbiased Estimate (BLUE) of a. parameter θ based on data Y is. 1.

### What is the difference between BLUP and blue?

In case of BLUE, unbiased means the expected value of a mean estimate for an individual equals its true value. This is a conditional mean. By contrast, in case of BLUP the expected mean over all individuals is equal to the expected mean over all true effects.

Can a biased estimator be consistent?

An estimator can be unbiased for all n but inconsistent if the variance doesn’t go to zero, and it can be consistent but biased for all n if the bias for each n is nonzero, but going to zero.

Is b1 unbiased?

As promised, b1 is unbiased for β1 and b0 is unbiased for β0. proc reg and proc glm fit regression models.

## What does blue mean econometrics?

Best Linear Unbiased Estimator
BLUE is an acronym for the following: Best Linear Unbiased Estimator. In this context, the definition of “best” refers to the minimum variance or the narrowest sampling distribution.

### What does blue stand for in OLS?

Under the GM assumptions, the OLS estimator is the BLUE (Best Linear Unbiased Estimator). Meaning, if the standard GM assumptions hold, of all linear unbiased estimators possible the OLS estimator is the one with minimum variance and is, therefore, most efficient.

Why is OLS the best unbiased estimator?

The Gauss-Markov theorem states that satisfying the OLS assumptions keeps the sampling distribution as tight as possible for unbiased estimates. The Best in BLUE refers to the sampling distribution with the minimum variance. That’s the tightest possible distribution of all unbiased linear estimation methods!

Is sample mean the best linear unbiased estimator?

Then the sample mean is not only BLUE but it is the best unbiased estimator for µ. – i.e. it is the best among all (even nonlinear) estimators.