Any econometrics whizzes here?

[Jules]

Adam Smith:

Thanks, but I pretty much understand what we are trying to do in this problem. The trouble I'm having is figuring out how to take into account this additional piece of information (i.e., this beta-one-star estimate from another data source).

Here's everything I know so far...

[Jules]

Originally posted by GP
Also, I don't understand how you can have variance of an estimate. I mean does beta correspond to the coefficent in a regression? And X to a variable?

Because the estimate is partially a function of the error term, epsilon, which is stochastic. Hence, the estimate will have some variance. And, yes, beta is the regression coefficient and X is an independent variable. But observe, for example, in the equation for beta-one-hat (the OLS estimate for beta-one). It is function of X and y, where we assume y is a linear function of X plus some error.

[Lawrence of Arabia]

You can make hella money off of econometric because very few people know how to do it.

[Adam Smith]

Jules:

V(Beta1hat) - V(Beta1tilde) is positive semi-definite means that you just proved Part A. If V(Beta1hat) is always at least as big, then V(Beta1tilde) is always at least as small.

GP:

The estimator has a variance because if you draw a different sample you will get a different value of the estimator.

[TCO]

Originally posted by Adam Smith
Jules:

V(Beta1hat) - V(Beta1tilde) is positive semi-definite means that you just proved Part A. If V(Beta1hat) is always at least as big, then V(Beta1tilde) is always at least as small.

GP:

The estimator has a variance because if you draw a different sample you will get a different value of the estimator.

I guess I think of variance as a charactistic of the sample set. And the goodness of fit would be an r-factor.

I totally defer to y'all's wisdom. Just trying to think about it in my simple terms.

Sure the regression coefficient would be different with a different sample set. But I don't know how that is a variance of an individual estimate. Seems like talking about the variance of an individual estimate of the mean. I guess you could talk about variance of the mean in general for several samples. But for one?

[Sten Sture]

Re: This is a job for ....

Originally posted by Adam Smith
The guts of this problem is showing that adding additional unbiased information to an estimator can't make you any worse off (ie no greater variance).

Thanks, Adam. That is the part that I needed.

[TCO]

Is this basically the Central Limit Thereom?