Suppose that X1,...,Xn iid∼ DE(µ,1), the “double exponential” distribution with mean µ and scale parameter 1 and with density f(x) = 1 2 e −|x−µ| I(−∞,∞)(x). Find an estimator of µ by the method of...

Suppose that X1,...,Xn

iid∼ DE(µ,1), the “double exponential” distribution with mean µ and

scale parameter 1 and with density

f(x) = 1

2

e

−|x−µ|

I(−∞,∞)(x).

Find an estimator of µ by the method of moments, and identify its asymptotic distribution.