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Multiple Regression Analysis: OLS Asymptotics

Q: When is an estimator consistent and what MLR has to hold?

^Bj is a consistent estimator of Bj if we can make it 'arbitrarily close' to Bj by collecting 'enough' data MLR4 (Zero mean and zero correlation): E(u)=0 and cov(x(j),u)=0

Q: What do we mean with asymptotic normality and what assumptions suffice?

MLR1-MLR5 suffice to establish asymptotic normality of OLS estimators, which means that they are approximately normal in large samples.

Q: What does asymptotic efficiency mean?

It means 'best' in large samples among estimators in some appropriate class

4 important questions on Multiple Regression Analysis: OLS Asymptotics

What are the finite samples and how do they differ from the asymptotic?

MLR1-MLR4 (Unbiased)
MLR1-MLR5 (BLUE)
MLR1-MLR6 (Normal)
Properties hold approximately when the sample is large, because t and F distributions have their limits.

When is an estimator consistent and what MLR has to hold?

^Bj is a consistent estimator of Bj if we can make it "arbitrarily close" to Bj by collecting "enough" data
MLR4 (Zero mean and zero correlation): E(u)=0 and cov(x(j),u)=0