An estimator of 𝜎𝜎𝑖𝑖2 is given by 𝑒𝑒𝑖𝑖2 , the square of the OLS residual 𝑒𝑒𝑖𝑖 = 𝑦𝑦𝑖𝑖 − 𝑥𝑥𝑖𝑖′ 𝑏𝑏.
The square roots of the diagonal elements are the White standard errors.
Model for variance
𝜎𝜎𝑖𝑖2 = ℎ(𝑧𝑧𝑖𝑖′ 𝛾𝛾)
⋅ ℎ: a known function
⋅ 𝑧𝑧 = �1, 𝑧𝑧1 , … , 𝑧𝑧𝑝𝑝 �′, a vector of 𝑝𝑝 observed variables that influence the variances
⋅ 𝛾𝛾: a vector of 𝑝𝑝 unknown parameters
where 𝑣𝑣𝑖𝑖 > 0 is known and 𝜎𝜎 2 is an unknown scalar parameter.
Weighted least squares (WLS)
The transformed model satisfies assumptions 1 to 6.
Therefore, the best linear unbiased estimator (BLUE) of 𝛽𝛽 is obtained by applying least squares in the
transformed model.
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller Econometrino. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $9.11. You're not tied to anything after your purchase.