Category Archives: Mathematical Proofs

The Derivative of the Natural Logarithm

The derivative of the natural logarithm is defined the following way: The formal proof of the derivative is provided at the bottom of this post. The following example further explains the derivative of the natural logarithm. Remember that Advertisements

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Proof Gauss Markov Theorem

From a previous posts on the Gauss Markov Theorem and OLS we know that the assumption of unbiasedness must full fill the following condition

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Unbiased Estimator of Sample Variance – Vol. 2

Lately I received some criticism saying that my proof (link to proof) on the unbiasedness of the estimator for the sample variance strikes through its unnecessary length. Well, as I am an economist and love proofs which read like a … Continue reading

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The Gauss Markov Theorem

When studying the classical linear regression model, one necessarily comes across the Gauss-Markov Theorem. The Gauss-Markov Theorem is a central theorem for linear regression models. It states different conditions that, when met, ensure that your estimator has the lowest variance … Continue reading

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What is an indirect proof?

In economics, especially in theoretical economics, it is often necessary to formally prove your statements. Meaning to show your statements are correct in a logical way. One possible way of showing that your statements are correct is by providing an … Continue reading

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Proof of Unbiasedness of Sample Variance Estimator

Proof of Unbiasness of Sample Variance Estimator (As I received some remarks about the unnecessary length of this proof, I provide shorter version here) In different application of statistics or econometrics but also in many other examples it is necessary … Continue reading

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