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Approximate theory for linear regression design
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algorithms approximate theory ATM~A choose concave function consider constructing optimal design containing SC convex combination convex cone convex function convex hull convex set criterion function D-optimal defined denote depend on 9 design measure corresponding design measure putting design measure rj design point design problem design space SC discuss duality theory ellipsoid equivalent estimator of 9 example exists experimentation Fedorov Fisher's information matrix Gateaux derivative Hence induced design space interest iteration iV-observation design k x k matrix Kiefer least-squares estimator linear regression design logdet minimize n e H N-observation non-linear non-singular matrix Note observations optimal design measure optimal measure particular points of SC positive definite possible practical probability distribution Proof Pukelsheim 1980 random vector s x s Section sequentially constructed design Silvey singular information matrix step-length support points Suppose take the value Theorem 3.7 variance matrix vector with distribution verify W-algorithm xeSC