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Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators

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  • Li, Tong
  • Vuong, Quang

Abstract

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.

Suggested Citation

  • Li, Tong & Vuong, Quang, 1998. "Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 139-165, May.
    • Handle: RePEc:eee:jmvana:v:65:y:1998:i:2:p:139-165
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    References listed on IDEAS

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    1. Joel L. Horowitz & Marianthi Markatou, 1996. "Semiparametric Estimation of Regression Models for Panel Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(1), pages 145-168.
    2. Joel L. Horowitz & Marianthi Markatou, 1993. "Semiparametric Estimation Of Regression Models For Panel Data," Econometrics 9309001, University Library of Munich, Germany.
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