Two cross-validation criteria for SIR\({}_\alpha\) and PSIR\({}_\alpha\) methods in view of prediction
The sliced inverse regression technique SIR and its ``robustified'' version PSIR for fitting the single-index regression model \(y=f(x^\top\beta,\varepsilon)\) are considered. (Here \(f\) is an unknown link function to be estimated nonparametrically, \(x^\top\beta\) is the index.) The authors discuss the mixed SIR-I and SIR-II method, called SIR\({}_\alpha\) and PSIR\({}_\alpha\). Cross-validation criteria for the choice of the mixing parameter \(\alpha\) and the bandwidth in the Nadaraya-Watson estimator for \(f\) are proposed. Simulation results are presented for the model \(y=10+(x^\top\beta +C)^2+\varepsilon\), with \(x\) having standard Gaussian distribution in \(R^5\).
scientific article; zbMATH DE number 2118522
scientific article