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


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Statistics in Transition New Series

Polish Statistical Association

Central Statistical Office of Poland

Subject: Economics , Statistics & Probability


ISSN: 1234-7655
eISSN: 2450-0291





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VOLUME 21 , ISSUE 4 (August 2020) > List of articles

Special Issue

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

Takumi Saegusa

Keywords : confidence band, data integration, Gaussian process

Citation Information : Statistics in Transition New Series. Volume 21, Issue 4, Pages 144-158, DOI:

License : (CC BY-NC-ND 4.0)

Received Date : 31-January-2020 / Accepted: 30-June-2020 / Published Online: 15-September-2020



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.

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