We address function misspecification and model heterogeneity, two critical issues in empirical work. A nonparametric approach is proposed for single-index, binary-choice models when parametric models such as Probit and Logit are potentially misspecified. The new approach involves two steps: first, we estimate index coefficients using sliced inverse regression without knowing the conditional pro...

We propose a nonparametric approach for estimating single-index, binarychoice models when parametric models such as Probit and Logit are potentially misspecified. The new approach involves two steps: first, we estimate index coefficients using sliced inverse regression without specifying a parametric probability function a priori; second, we estimate the unknown probability function using kerne...

We employ Lasso shrinkage within the context of sufficient dimension reduction to obtain a shrinkage sliced inverse regression estimator, which provides easier interpretations and better prediction accuracy without assuming a parametric model. The shrinkage sliced inverse regression approach can be employed for both single-index and multiple-index models. Simulation studies suggest that the new...

We propose a new class of dimension reduction methods using the first two inverse moments, called Sliced Inverse Moment Regression (SIMR). We develop corresponding weighted chi-squared tests for the dimension of the regression. Basically, SIMR are linear combinations of Sliced Inverse Regression (SIR) and the method using a new candidate matrix which is designed to recover the entire inverse se...

The concept of inverse regression has turned out to be quite useful for dimension reduction in regression analysis problems. Using methods like sliced inverse regression (SIR) and directional regression (DR), some high-dimensional nonlinear regression problems can be turned into more tractable low-dimensional problems. Here, the usefulness of inverse regression for identification of nonlinear d...

We apply the univariate sliced inverse regression (SIR) to survival data. Our approach is different from the other papers on this subject. The right-censored observations are taken into account during the slicing of the survival times by assigning each of them with equal weight to all of the slices with longer survival. We test this method with different distributions for the two main survival ...