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.
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References
Bonneu, M., Delecroix, M. and Hristache, M. (1995), “Semiparametric estimation of generalized linear models”, preprint, CREST, Paris.
Delecroix, M. and Hristache, M. (1999), “M-estimateurs semi-paramétriques dans les modèles à direction révélatrice unique”, Bulletin of the Belgian Mathematical Society, 6, 161–185.
Delecroix, M., Hristache, M. and Patilea, V. (1999), “Optimal smoothing in semiparametric index approximation of regression functions”, working paper n∘9952, CREST, Paris.
Härdle, W., Hall, P. and Ichimura, H. (1993), “Optimal smoothing in single-index models”, Annals of Statistics, 21, 157–178.
Härdle, W., Hart, J.D., Marron, J.S. and Tsybakov, A.B. (1992), “Bandwidth choice for average derivative estimation”, Journal of the American Statistical Association, 87, 218–226.
Härdle, W. and Stoker, T.M. (1989), “Investigating smooth multiple regression by the method of average derivatives”, Journal of the American Statistical Association, 84, 986–995.
Härdle, W. and Tsybakov, A.B. (1993), “How sensitive are average derivatives”, Journal of Econometrics, 58, 31–48.
Ichimura, H. (1993), “Semiparametric least squares (SLS) and weighted SLS estimation of single-index models”, Journal of Econometrics, 58, 71–120.
Klein, R.L. and Spady, R.H. (1993), “An efficient semiparametric estimator for binary response models”, Econometrica, 61, 387–421.
Newey, W.K. and Stoker, T.M. (1993), “Efficiency of weighted average derivative estimators and index models”, Econometrica, 61, 1199–1223.
Powell, J.L., Stock, J.M. and Stoker, T.M. (1989), “Semiparametric estimation of index coefficients”, Econometrica, 57, 1403–1430.
Robinson, P.M. (1995), “The normal approximation for semiparametric averaged derivatives”, Econometrica, 63, 667–680.
Sherman, R.P. (1994), “U-processes in the analysis of a generalized semiparametric regression estimator”, Econometric Theory, 10, 372–395.
Stoker, T.M. (1986), “Consistent estimation of scaled coefficients”, Econometrica, 54, 1461–1481.
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Hristache, M. Are Efficient Estimators in Single-Index Models Really Efficient? A Computational Discussion. Computational Statistics 17, 453–464 (2002). https://doi.org/10.1007/s001800200119
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DOI: https://doi.org/10.1007/s001800200119