Timeline for Using White's Robust Co-variance Matrix vs Weighted Least Squares to correct for heteroscedasticity
Current License: CC BY-SA 4.0
9 events
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| Jan 31, 2019 at 15:42 | comment | added | Ryan Simmons | @StatsStudent Thanks for clarifying! I am familiar with the Gauss-Markov theorem. Makes sense to refer to OLS as a Gauss-Markov model, though just wasn't familiar with that precise usage. Interesting! | |
| Jan 31, 2019 at 15:33 | comment | added | StatsStudent | @RyanSimmons, that should have read "Gauss-Markov model" instead of just "Markov-Model." This is the term you'll find in pure statistics due to the Gauss-Markov theorem. I'm travelling today, so don't my references in front of me, but I think you'll find this reference in "Applications of Linear and Nonlinear Models Fixed Effects, Random Effects, and Total Least Squares." by Grafarend and Awange and in "A Primer on Linear Models" by John F. Monahan. I'll also try to get to the the other Ryan's (the OP's) questions later today if time allows when I'm back to a computer. | |
| Jan 31, 2019 at 15:20 | history | edited | StatsStudent | CC BY-SA 4.0 |
changed "Markov-Model" to Gauss-Markov model to provide clarity.
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| Jan 31, 2019 at 15:10 | comment | added | Ryan Simmons | Perhaps this is an issue of different fields having different terminology/notation, but I've never heard a linear regression described as a "Markov model" before. I would use "Markov model" to describe an entirely different class of techniques. This is a bit of an aside from the main point, because the rest of your answer is wonderful, but I was curious as to whether you could elaborate or provide a reference for a linear regression being referred to as such. Could take it to the chat if mods deem it too extraneous. | |
| Jan 31, 2019 at 14:53 | comment | added | Ryan Boch | @StatsStudent. This is actually the exact book I am using that raised this question. What you have stated is fairly clear, but I'm still not understanding how this affects the confidence intervals for the mean response. The bottom of page 426 states that weighted least squares uses the modified variance for the mean response confidence intervals, but page 427 seems to imply that White's estimator is only used for coefficient std errors. I may not be connecting things through. I will post some code above which may help. | |
| Jan 30, 2019 at 22:03 | history | edited | StatsStudent | CC BY-SA 4.0 |
edited body
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| Jan 30, 2019 at 21:56 | comment | added | StatsStudent | @HeteroskedasticJim, because $\boldsymbol{X}$ and $\boldsymbol{\beta}$ are considered constants in the Markov Model. | |
| Jan 30, 2019 at 0:45 | comment | added | Heteroskedastic Jim | How is this possible? $Var(\boldsymbol{Y})=Var\left(\boldsymbol{X\beta}+\boldsymbol{\epsilon}\right)=Var(\boldsymbol{\epsilon})=\boldsymbol{I}\sigma^{2}$ | |
| Jan 29, 2019 at 23:37 | history | answered | StatsStudent | CC BY-SA 4.0 |