# Questions tagged [gauss-markov-theorem]

The Gauss-Markov theorem gives the conditions for the best (minimum-variance) linear unbiased estimator of a linear model.

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### If the errors are homogenous but non-normal, can the linear estimator be BLUE?

Under the Gauss-Markov assumptions, the requirements for OLS to be BLUE are: Linearity: The estimator must be a linear function of the data Unbiasedness: The expected value of the estimator should ...
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### OLS vs MLE when errors are not normally distributed (Laplace distributed)

We say that under assumptions of the Gauss-Markov theorem, OLS is BLUE. The Gauss-Markov theorem doesn't mention the normality of errors. If the errors are distributed as per the Laplace distribution,...
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### Why would bootstrap OLS standard errors differ from ML estimate?

Let's say I have a regression dataset (paired x and y) such that the response variable (y) has an unknown distribution (but definitely not Gaussian) and is large enough such that the central limit ...
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### What are the consequences of the violation of Gauss-Markov assumptions?

If these are the assumptions: A(1) E(ϵi)=0 for all i A(2) ϵi and xi´ are independent for all i,i´ A(3) var(ϵi)=σ² < ∞ for all i A(4) cov(ϵi,ϵi´)=0 for all i ≠ i´ What does the violation of these ...
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### Using the unbiasedness assumption in the proof of the Gauss-Markov Theorem

In what follows $y = (y_1,\dots,y_n)$ is a $n\times 1$ vector of random variables and $X = (x_{ij})$ is a $n\times d$ random matrix ($n>d$ tipically) with $\text{rank}(X)=d$ with probability 1. ...
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### Does the Gauss-Markov Theorem state that OLS is the only BLUE estimator?

I was reading through the proof on wiki. Which is the following. \begin{align} \operatorname{E} \left[ \tilde\beta \right] &= \operatorname{E}[Cy] \\ &= \operatorname{E} \left [\left ((X'X)^{-...
1 vote
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### Random Sampling: Weak and Strong Exogenity

$Y \ = \ X' \beta \ + \ e$ Where $Y = (y_1, ..., y_n)$ and $\beta = (\beta_0,..., \beta_k)$. Why would Weak Exogenity under random sampling produce Strong Exogenity? I know that weak exogenity is ...
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### Exogenity: What does E(eX) really mean and why is it used?

What does it mean to talk about the expectation of the product of the error term and an independent variable? Like, why do we even need to mention $E(e_i X_{ik})$? What is it actually describing or ...
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1 vote
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### Finding Best Linear Unbiased Estimator

I have the doubt that if Gauss Markov theorem is applicable here since the Variance is not constant in the model. Without Gauss Markov Theorem, how can we obtain BLUE?
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