Single Index Models

Abstract

This chapter describes single-index models for conditional mean and quantile func- tions. Single-index models relax some of the restrictive assumptions of familiar parametricmodels, such as linear models and binary probit or logitmodels. In addi- tion, single-index models achieve dimension reduction and, thereby, greater estima- tion precision than is possible with fully nonparametric estimation of E(Y|X = x) when X is multidimensional. Finally, single-indexmodels are often easy to compute, and their results are easy to interpret. Sections 2.1–2.9 present a detailed discussion of single-index models for conditional mean functions. Conditional quantile func- tions are discussed in Section 2.9.