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 to estimate the variance of a sample. The estimator of the variance, see equation (1) is normally common knowledge and most people simple apply it without any further concern. The question which arose for me was why do we actually divide by n-1 and not simply by n? In the following lines we are going to see the proof that the sample variance estimator is indeed unbiased. Continue reading Proof of Unbiasedness of Sample Variance Estimator

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Log-Linearizing

Log-Linearizing

What exactly is happening when we linearize a model? Well, the answer is simple, we basically approximate non-linear equations with linear once. In context of macroeconomics we may have models which are non-linear. Thus in order to solve them there is need to put them in a linear form. In the following we are going to see how to log-linearizing a model by the means of a (very) simple example. Continue reading Log-Linearizing