Simple Estimators for Invertible Index Models

Hyungtaik Ahn, Hidehiko Ichimura, James L. Powell, Paul A. Ruud

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

This article considers estimation of the unknown linear index coefficients of a model in which a number of nonparametrically identified reduced form parameters are assumed to be smooth and invertible function of one or more linear indices. The results extend the previous literature by allowing the number of reduced form parameters to exceed the number of indices (i.e., the indices are “overdetermined” by the reduced form parameters. The estimator of the unknown index coefficients (up to scale) is the eigenvector of a matrix (defined in terms of a first-step nonparametric estimator of the reduced form parameters) corresponding to its smallest (in magnitude) eigenvalue. Under suitable conditions, the proposed estimator is shown to be root-n-consistent and asymptotically normal, and under additional restrictions an efficient choice of a “weight matrix” is derived in the overdetermined case.

Original languageEnglish (US)
Pages (from-to)1-10
Number of pages10
JournalJournal of Business and Economic Statistics
Volume36
Issue number1
DOIs
StatePublished - Jan 2 2018
Externally publishedYes

Keywords

  • Invertible models
  • Multinomial response
  • Semiparametric estimation
  • Single index models

ASJC Scopus subject areas

  • Statistics and Probability
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

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