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Are Efficient Estimators in Single-Index Models Really Efficient? A Computational Discussion

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  • Marian Hristache

    (ENSAI and CREST)

Abstract

Summary 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.

Suggested Citation

  • Marian Hristache, 2002. "Are Efficient Estimators in Single-Index Models Really Efficient? A Computational Discussion," Computational Statistics, Springer, vol. 17(4), pages 453-464, December.
    • Handle: RePEc:spr:compst:v:17:y:2002:i:4:d:10.1007_s001800200119
    DOI: 10.1007/s001800200119
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