Hostname: page-component-68945f75b7-72kh6 Total loading time: 0 Render date: 2024-08-06T03:15:45.460Z Has data issue: false hasContentIssue false
  • English
  • Français

A PERMUTATION-BASED ESTIMATOR FOR MONOTONE INDEX MODELS

Published online by Cambridge University Press:  03 April 2008

Debopam Bhattacharya
Debopam Bhattacharya*
Affiliation:
Dartmouth College
*
Address correspondence to Debopam Bhattacharya, Department of Economics, 301 Rockefeller Hall, Dartmouth College, Hanover, NH 03755, USA; e-mail: debopam.bhattacharya@dartmouth.edu.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper shows that the finite-dimensional parameters of a monotone-index model can be estimated by minimizing an objective function based on sorting the data. The key observation guiding this procedure is that the sum of distances between pairs of adjacent observations is minimized (over all possible permutations) when the observations are sorted by their values. The resulting estimator is a generalization of Cavanagh and Sherman's monotone rank estimator (MRE) (Cavanagh and Sherman, 1998, Journal of Econometrics 84, 351–381) and does not require a bandwidth choice. The estimator is -consistent and asymptotically normal with a consistently estimable covariance matrix. This least-squares estimator can also be used to estimate monotone-index panel data models. A Monte Carlo study is presented where the proposed estimator is seen to dominate the MRE in terms of mean-squared error and mean absolute deviation.

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 3 , June 2008 , pp. 795 - 807
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Cavanagh, C. ’ Sherman, R.P. (1998) Rank estimators for monotonic index models. Journal of Econometrics 84, 351–381.CrossRefGoogle Scholar
Horowitz, J.L. (1992) A smoothed maximum score estimator for the binary response model. Econometrica 60, 505–531.CrossRefGoogle Scholar
Sherman, R.P. (1993) The limiting distribution of the maximum rank correlation estimator. Econometrica 61, 123–137.CrossRefGoogle Scholar
Sherman, R.P. (1994) Maximal inequalities for degenerate U-processes with applications to optimization estimators. Annals of Statistics 22, 439–459.CrossRefGoogle Scholar