Consider the linear model yi = xiB + e = B1 + B2xi2 + ... + Bkxik + ei, i = 1, ..., n, or in matrix notation Y =XB + e.
Consider the linear model X = Z pie + u where Z is a matrix n * m, X is a matrix n * k and pie is a matrix m * k. Assume that
1. E (x'ixi) has full column rank;
2. E (ei/xi) = g (xi), , i =1, ..., n;
3. E (ei4) < infinity and E (xij/4) < infinity, i =1, ..., n; j =1, ..., k;
4. E (ui/zi) = 0, i = 1, ..., n;
A.) Let m = k and assume that rank pie = k. Derive a consistent estimator for B. Derive the asymptotic distribution of the estimator.
B.) Let m > k find a consistent estimator of B and his distribution.
C.) What happen if m = k and E (X'Z) has rank j < k?
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