Deconvolution From Two Order Statistics

34 Pages Posted: 9 Jan 2021 Last revised: 28 Jan 2022

See all articles by JoonHwan Cho

JoonHwan Cho

University of Toronto - Department of Economics

Yao Luo

University of Toronto - Department of Economics

Ruli Xiao

Indiana University Bloomington - Department of Economics

Date Written: November 18, 2020

Abstract

Economic data are often truncated by ranking and contaminated by measurement errors. We study the identification of the distributions of a latent variable of interest and its measurement errors using a subvector of order statistics of repeated measurements. Kotlarski's lemma is inapplicable due to dependence in the order statistics of measurement errors. Exploiting the ratio of characteristic functions of order statistics, we show observing two order statistics are sufficient to identify the underlying distributions nonparametrically. We adapt an existing simulated sieve estimator to our setting and illustrate its performance in finite samples.

Keywords: Measurement Error, Order Statistics, Nonparametric Identification, Spacing, Cross-Sum

JEL Classification: C14, D44

Suggested Citation

Cho, JoonHwan and Luo, Yao and Xiao, Ruli, Deconvolution From Two Order Statistics (November 18, 2020). Available at SSRN: https://ssrn.com/abstract=3733211 or http://dx.doi.org/10.2139/ssrn.3733211

JoonHwan Cho (Contact Author)

University of Toronto - Department of Economics ( email )

150 St. George Street
Toronto, Ontario M5S3G7
Canada

Yao Luo

University of Toronto - Department of Economics ( email )

150 St. George Street
Toronto, Ontario M5S3G7
Canada

Ruli Xiao

Indiana University Bloomington - Department of Economics ( email )

Wylie Hall
Bloomington, IN 47405-6620
United States

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