Consider the Huber XXXXXXXXXXestimator, for which ψ(x) = xI(|x| ≤ k) + k · sign(x)I(|x| > k) for some finite k > 0. Suppose that IEF |X| α 0 (not necessarily ≥ 1). What is the minimum sample size n,...

Consider the Huber (1964) estimator, for which ψ(x) = xI(|x| ≤ k) + k · sign(x)I(|x| > k) for some finite k > 0. Suppose that IEF |X| α <> 0 (not necessarily ≥ 1). What is the minimum sample size n, such that the Huber estimator has a finite rth moment, for some r > 0? Compare the situation with that of the sample mean.