1.8 Asymptotic Theory Flashcards
What is asymptotic theory?
It considers the properties of random variables in the case where the sample size is allowed to tend towards infinity
Convergence in distribution
If the sample size T is big enough the distribution of ZT will be indistinguishable from that of Z
Convergence in probability
If the sample size is large enough ZT will take the same value as Z
When are convergence of distribution and convergence of probability the same?
When we have a constant
What is the relationship between convergence of distribution and convergence of probability?
Convergence of probability is a stronger concept. Convergence of probability implies convergence of distribution but the converse isn’t true
What is the weak law of large numbers?
It is an application of convergence in probability in the degenerate case. It considers the case where ZT converged to the expected value as T goes to infinity
When can the WLLN be extended to dependent random variables?
When the Variable of ZT goes to zero as T goes to infinity
Are unbiased estimators always consistent?
Nope
Are consistent estimators always unbiased?
Nope
What does the CLT show about the standardised sums of random variables?
That they are asymptotically normally distributed even though the random variables themselves aren’t individually normal
Is the OLS estimator of beta hat consistent?
Yes
Is the OLS estimator of the variance consistent?
Yes
