Are Efficient Estimators in Single-Index Models Really Efficient? A Computational Discussion
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In this paper, we consider estimators of the finite dimensional parameter θ0 in the single-index regression model defined by: E(Y∣X) = E(Y∣Xθ0). We use semiparametric weighted M-estimators defined as maximizing a pseudo-likelihood based on the linear exponential family and which have been shown to be asymptotically efficient. We discuss the choice of the pseudo-likelihood and the practical efficiency of these estimators, using computational arguments. We show that for a large but reasonable sample size, the asymptotically efficient estimator works better than the usual ones.
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