Suppose that we have a sample (Y, X), i = 1,...,n, and consider the following linear...

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Suppose that we have a sample (Y, X), i = 1,...,n, and consider the following linear regression model: We estimate 3 by WLS: Y = XB+e. -1 (LXX) LXX. i=1 8 = for some hi, i = 1,..., N, where h = o(Xi) for some positive function o(.).. However, it turns out that E(e? | X) #hi. (a) Y = XB+e. (b) (Y, X), i = 1,...,n is i.i.d. Prove the consistency of the WLS estimator and derive the asymptotic distribution under the following set of conditions. (3) (c) E(X,X/h,) exists and is invertible. (d) E(e, | X) = 0. (e) (X, ei) has at least fourth-order moments. Condition (e) should read (Xi/hi,ei/hi) has at least fourth-order moments. Suppose that we have a sample (Y, X), i = 1,...,n, and consider the following linear regression model: We estimate 3 by WLS: Y = XB+e. -1 (LXX) LXX. i=1 8 = for some hi, i = 1,..., N, where h = o(Xi) for some positive function o(.).. However, it turns out that E(e? | X) #hi. (a) Y = XB+e. (b) (Y, X), i = 1,...,n is i.i.d. Prove the consistency of the WLS estimator and derive the asymptotic distribution under the following set of conditions. (3) (c) E(X,X/h,) exists and is invertible. (d) E(e, | X) = 0. (e) (X, ei) has at least fourth-order moments. Condition (e) should read (Xi/hi,ei/hi) has at least fourth-order moments.