4. Let the common PDF be the folded normal distribution 2 exp 1 2 (x)2 I[,)(x). Verify that the best equivariant estimator

4. Let the common PDF be the folded normal distribution

2

π

exp



−1 2

(x−μ)2



I[μ,∞)(x).

Verify that the best equivariant estimator of μ under quadratic loss is given by

ˆμ = X− exp{−n2

(X(1)

−X)2}

√

2nπ

) √

n(X(1)

−X)

0

√1 2π

exp(−z2/2)dz

*.