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Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators

✍ Scribed by Tong Li; Quang Vuong

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 413 KB
Volume: 65
Category: Article
ISSN: 0047-259X
DOI: 10.1006/jmva.1998.1741

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✦ Synopsis

This paper considers the nonparametric estimation of the densities of the latent variable and the error term in the standard measurement error model when two or more measurements are available. Using an identification result due to Kotlarski we propose a two-step nonparametric procedure for estimating both densities based on their empirical characteristic functions. We distinguish four cases according to whether the underlying characteristic functions are ordinary smooth or supersmooth. Using the loglog Law and von Mises differentials we show that our nonparametric density estimators are uniformly convergent. We also characterize the rate of uniform convergence in each of the four cases.

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