Consider the procedure of Sec. 10.4.1. Assume that X1j, X2j, ..., Xkj (for j = 1, 2, ...,...

Consider the procedure of Sec. 10.4.1. Assume that X_1j, X_2j, ..., X_kj (for j = 1, 2, ..., n₀) has a multivariate normal distribution with covariance matrix ∑, which has the property of sphericity. Then it can be shown [see Lemma 2 in Nelson and Matejcik (1995)] that S² is distributed as , where is a chi-square random variable with ν degrees of freedom. Under these assumptions, show that S² is an unbiased estimator of Var(X_ij – X_lj) = 2τ².