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8 votes

Is OLS asymptotically the best estimator even without gaussian error?

The OLS estimate and the MLE will asymptotically approach normal distributions. But, no, they will not have the same variance, and the OLS estimate does not need to become (asymptotically) the UMVU ...
Sextus Empiricus's user avatar
4 votes
Accepted

In linear regression, what's the asymptotic distribution of the error variance estimator?

This answer extends the sample mean case studied in Asymptotic distribution of $\sqrt{n}(\hat{\sigma}_{1}^{2}-\sigma^2)$ to the linear regression setup. Let us assume an iid sample from a linear model ...
Christoph Hanck's user avatar
2 votes

Understanding differences in collinearity across Stata commands

reghdfe is different because, by default, it tries to deal with collinearity. I don't have Stata, but a little Googling found pages about this. It should be in the documentation for the program. The ...
Peter Flom's user avatar
  • 122k
2 votes
Accepted

Granular difference-in-differences with non-repeating unit of observation

I recommend the following notation, $$ Y_{pst} = \beta_1 T_s + \beta_2 A_t + \beta_3 (T_s \times A_t) + \epsilon_{pst}, $$ where you observe some characteristic of job posting $p$ in state $s$ and ...
Thomas Bilach's user avatar
2 votes
Accepted

How Does Serial Correlation Cause OLS to remain unbiased (even in cross -sectional data)

Unbiased here means unbiased over repeated draws of the data from the same generating process. If you run the data generating process again you will get different $u_j$. They will be correlated in the ...
Thomas Lumley's user avatar
1 vote

statsmodels: Update OLS' degrees of freedom when absorbing 3+ fixed effects

In R, the following correction restores equality of the (nonrobust) s.e.s of the residual-based regression to the fixed-effects based ones: ...
Christoph Hanck's user avatar
1 vote

Matrix decomposition with constraints and weighted least squares

i would think this could be done relatively easily using an unconstrained nonlinear least squares optimiser such as levenberg marquardt you can turn your probability constraints on f_j, into ...
seanv507's user avatar
  • 7,002
1 vote

In linear regression, what's the asymptotic distribution of the error variance estimator?

$\hat{\sigma}^2 \sim \Gamma(\nu/2, \nu/(2 \sigma^2))$ (using the parameterizaton of the Gamma distribution in terms of shape and rate parameter), where $\nu$ is the degrees of freedom and $\sigma^2$ ...
Björn's user avatar
  • 33k
1 vote

Special case of Frisch-Waugh-Lowell theorem

I figured it out, the idea is just matrix multiplication. Obtain $b_1,b_2$ by regressing $Y$ on $X_1,X_2$. We then have $$Y=X_1b_1+X_2b_2+MY.\tag{1}\label{1}$$ Obtain $\tilde\beta_1$ by regressing $Y$ ...
Chang Henry's user avatar

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