Question

Obtain maximum likelihood estimator f x =1 /theta*e^-x/theta

Answer 1

Step-by-step explanation:

I'm given f(x;θ)=12e−|x−θ|, −∞<x<∞ and 0<θ<∞. I want to find the maximum likelihood estimator of θ. I found:

lnL(θ;x1,...,xn)=−nln2−∑|xi−θ|

Usually I would differentiate and find the maximum. Here differentiation does not work. But by inspection, ∑|xi−θ| is always positive so L has a maximum when ∑|xi−θ|=0. But how can I express θ in terms of the xi's?