Laplace center MLE for forecast errors

Question

Forecast errors are modeled as Laplace centered at $\mu$ with known scale $b$ , density $f(x \mid \mu) = \dfrac{1}{2b} e^{-|x - \mu|/b}$ . Five errors are recorded: -2, 0, 3, 5, 11.

What is the maximum likelihood estimate of $\mu$ ?

Accepted Answer

Maximizing the Laplace log-likelihood means minimizing \sumi xi - \mu, which the sample median achieves. Sorting gives -2, 0, 3, 5, 11, and the middle value is \hat\mu = 3. Takeaway. For any Laplace location problem, sort the data and read off the median.

Laplace center MLE for forecast errors

Your answer

More Statistics questions