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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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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Question regarding a specific Gauss-Markov assumption

I am studying the Gauss–Markov assumptions. What is the intuition as to why the right hand side implies the left hand side?
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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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1answer
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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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Is Least Squares estimator for linear model the unique minimum variance unbiased estimator for a linear model?

I am following Linear Modfels in Statistics, Rencher & Schaalje, 2nd Edicition for the proof of Gauss-Markov Theorem (Theorem 7.3d, Page 146). I understand how least squares estimator $\mathbf{\...
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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)^{-...
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83 views

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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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?