# 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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### 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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### Conditional exogeneity when regressors are causally, linearly related

Let's say there is a multiple regression: $$Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + \beta_3X_3 + \beta_4X_4 + \beta_5X_5+U.$$ I know that conditional exogeneity implies that the error terms are mean ...
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### Is this regression impossible because of full rank assumption violation? [duplicate]

If there are four variables each with five observations: X1 X2 X3 X4 5 3 0 2 0 9 -9 0 3 1 0 2 7 3 0 4 5 2 0 3 Why can't you regress a dependent ...
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### Minimize MSE for only some parameters

Suppose I have a structural model parameterized by some $\theta = (\beta_i)_{i=1}^n$, but I am only interested in obtaining an unbiased/consistent/low variance estimator for $\beta_1$. For example, ...
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### Where does the linear regression assumption that the errors are uncorrelated enter into the proof of Gauss Markov and that Least Squares is BLUE?

I often see that the "Spherical Error" assumption is invoked for Gauss Markov. One of the parts of the assumption is that the variance is constant given $X$. The other is usually that the ...
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### How is zero conditional mean assumption "stronger" than uncorrelated assumption?

I am trying to understand what the zero conditional mean assumption ($\mathbb{E}[u\vert X]=0$) encompasses in addition to a zero-correlation assumption ($\text{Corr}(X,u)=0$). I assume it must be &...
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### Normality test vs Gauss Markov assumption for panel data

I am doing fixed effect regression after conducting hausmann test on panel data. I received significant results in line with what's expected for my model. My data set has around 6000 observations and ...
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### How Does Random Sampling Imply No Serial Correlation with Cross-Sectional Data?

I'm trying to prove that, under the random sampling, linear in parameters, and exogeneity Gauss-Markov assumptions, the error terms in $y=\beta_0+\beta_1x_1+\dots+\beta_kx_k+u$ are uncorrelated when ...
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### Gauss-Markov theorem explanation (linear regression)

I have attatched an excerpt from my linear modelling lecture notes, this is the statement of the Gauss-Markov theorem, trouble is it goes into no more detail after this (not even explaining what the ... 53 views

### Gauss-Markov with $p>n$

Let $p$ be the number of parameters in a linear regression model, let $n$ be the number of observations, and let $p>n$. $$\mathbb E[Y\vert X] = \beta_0 +\beta_1X_1 +...+\beta_pX_p$$ Does the Gauss-...
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### If the error terms in a regression setting are not observed, how can we ensure they're normally distributed?

According to the G-M assumptions, we should assume spherical errors. But my understanding is the errors -- as measured by the vertical distance from the true line of best fit to the response ...
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### OLS is BLUE (or BUE) to minimize MSE. Is quantile regression is BLUE to minimize MAE?

The Gauss-Markov theorem considers "best" as "lowest mean square error (MSE)" and a recent version of the theorem shows OLS is not only BLUE but also BUE: https://www.ssc.wisc.edu/~...
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### What is the benefit of regression with student-t residuals over OLS regression? [duplicate]

Sometimes I see advice to fit regressions with student-t residuals rather than using OLS (which is equivalent to assuming normally distributed residuals) if the distribution of the residuals is heavy-...
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### Proof of Gauss-Markov Theorem: Unaccountable Line

I'm trying to follow Faraway's proof of the Gauss-Markov model in his book Linear Models with R, 2nd Ed., on pages 22-23, but I have been having numerous difficulties. The latest difficulty is thick ...
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### Estimable Function Definition: Why $\forall \beta?$

I am reading Linear Models with R, 2nd Ed., by Julian J. Faraway, and on page 22, section 2.8 on the Gauss-Markov Theorem, he defines an estimable linear combination as follows: A linear combination ...
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### Unbiased least squares estimate for GM Theorem

In order to prove the Gauss-Markov Theorem, we first have to show that the OLS estimate $\hat{\theta}$ is an unbiased estimator. From what Im reading on Internet and some textbooks, these are the main ...
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### Is any Gauss-Markov assumption violated by the simple OLS regression transformation?

I am creating a simple linear model with the following form: $$y_i/x_i = \alpha + \beta x_i + u_i$$ The response variable has different name other than $y/x$, but it is essentially normalized by X ...
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### Generalized Least Square When Disturbance Covariance Matrix Is Rank Deficient

I cannot find any general results on the following Generalized Least Square (GLS) problem. Let $Y = X\beta + E$, where $X$ is deterministic and of full column rank $k$, and $E$ is of zero mean, with a ...
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### (Why) Are stepwise regression coefficients biased?

Issues with stepwise regression are known to statisticians. It yields R-squared values that are badly biased to be high. The F and chi-squared tests quoted next to each variable on the printout do ...
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### linearity in parameter assumption - implication for the Gauss-Markov theorem [closed]

Even if a similar question has been asked many times, I have not been able to understand the consequences of non linearity in parameter in relation to the Gauss-Markov theorem. In this question ...
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### Quadratic Form in Gauss-Markov Theorem

The following is the derivation of the Gauss-Markov Theorem in Greene's Econometric Analysis (8th ed.) I am trying to understand two points about the passage in yellow about the quadratic form. Why ...
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### Gauss-Markov and Asymptotic Properties

Is it true that Gauss-Markov assumptions (i.e. linearity, full rank, strict exogeneity, and $\sigma^2 I$) can imply "consistency" and "asymptotic normality" of the OLS estimator? ...
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