Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators

Tong Li, Quang Vuong

    Research output: Contribution to journalArticlepeer-review


    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.

    Original languageEnglish (US)
    Pages (from-to)139-165
    Number of pages27
    JournalJournal of Multivariate Analysis
    Issue number2
    StatePublished - May 1998


    • Fourier transformation
    • Measurement error model
    • Multiple indicators
    • Nonparametric density estimation
    • Uniform convergence rate

    ASJC Scopus subject areas

    • Statistics and Probability
    • Numerical Analysis
    • Statistics, Probability and Uncertainty


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