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ȯɽ¥¿¥¤¥È¥ë¡§The Isotonic-Regression Based Least Squares Estimation of Semiparametric Linear Index Models

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Isotonic Regression (IR) is a nonparametric method to estimate functions by direct minimization of mean squared errors over a functional set with shape restrictions. The IR is fast¡¤ efficient and free from tuning parameters such as kernel bandwidths. In this paper¡¤ a new class of the IR-based estimators for the single index model is proposed. The class includes the Semiparametric Least Squares (SLS) estimation¡¤ the Semiparametric Method-of-Moments (SMM) estimation¡¤ and the Iterative Least Squares (ILS) estimation. The paper mainly investigate large sample properties of these estimators¡¤ in particular¡¤ the cubic convergence rate of the SLS estimator¡¤ root-n asymptotic normality of the SMM estimator¡¤ and near semiparametric efficiency of the ILS estimator.

JEL classification: C14; C25

KEYWORDS: Single Index Models; Binary Choice Models; Isotonic Regression; Semiparametric Least Squares Estimation; Iterative Least Squares Estimation

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