We consider estimation of the regression parameter in the single index model where the link function $\psi$ is monotone. For this model it has been proposed to estimate the link function nonparametrically by the monotone least square estimate $\hat\psi_{n\alpha}$ for a fixed regression parameter $\alpha$ and to estimate the regression parameter by minimizing the sum of squared deviations $\sum_i\{Y_i-\hat\psi_{n\alpha}(\alpha^T X_i)\}^2$ over $\alpha$, where $Y_i$ are the observations and $ X_i$ the corresponding covariates... (read more)

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- STATISTICS THEORY