Simple Estimators for Monotone Single Index Models

Hyungtaik Ahn, Virginia Polytechnic University

Hidehiko Ichimura, University of Pittsburgh

James L. Powell, Princeton University

In this paper, estimation of the coefficients in a "single-index" regression model is considered under the assumption that the regression function is a smooth and strictly monotonic function of the index. The estimation method follows a "two-step" approach, where the first step uses a nonparametric regression estimator for the dependent variable, and the second step estimates the unknown index coefficients (up to scale) by an eigenvector of a matrix defined in terms of this first-step estimator. The paper gives conditions under which the the proposed estimator is root-n-consistent and asymptotically normal.

Key Words: Semiparametric estimation, single index model, two-step estimation

JEL Classification: C1, C4