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 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

The Gauss-Markov Theorem is telling us that in a regression model, where the expected value of our error terms is zero, and variance of the error terms is constant and finite and and are uncorrelated for all and the least … 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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