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Confidence bands for a distribution function with merged data from multiple sources

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  • Saegusa Takumi

    (University of Maryland, ; Maryland, ; United States)

Abstract

We consider nonparametric estimation of a distribution function when data are collected from multiple overlapping data sources. Main statistical challenges include (1) heterogeneity of data sets, (2) unidentified duplicated records across data sets, and (3) dependence due to sampling without replacement from a data source. The proposed estimator is computable without identifying duplication but corrects bias from duplicated records. We show the uniform consistency of the proposed estimator over the real line and its weak convergence to a Gaussian process. Based on these asymptotic properties, we propose a simulation-based confidence band that enjoys asymptotically correct coverage probability. The finite sample performance is evaluated through a simulation study. A Wilms tumor example is provided.

Suggested Citation

  • Saegusa Takumi, 2020. "Confidence bands for a distribution function with merged data from multiple sources," Statistics in Transition New Series, Statistics Poland, vol. 21(4), pages 144-158, August.
    • Handle: RePEc:vrs:stintr:v:21:y:2020:i:4:p:144-158:n:15
    DOI: 10.21307/stattrans-2020-035
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    References listed on IDEAS

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    1. Nilanjan Chatterjee & Yi-Hau Chen & Paige Maas & Raymond J. Carroll, 2016. "Constrained Maximum Likelihood Estimation for Model Calibration Using Summary-Level Information From External Big Data Sources," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 107-117, March.
    2. N. E. Breslow & N. Chatterjee, 1999. "Design and analysis of two‐phase studies with binary outcome applied to Wilms tumour prognosis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(4), pages 457-468.
    3. Niels Keiding & Thomas A. Louis, 2016. "Perils and potentials of self-selected entry to epidemiological studies and surveys," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(2), pages 319-376, February.
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