# 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