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Estimation of Poisson mean with under‐reported counts: a double sampling approach
Author(s) -
Sengupta Debjit,
Banerjee Tathagata,
Roy Surupa
Publication year - 2020
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/anzs.12308
Subject(s) - mathematics , statistics , estimator , confidence interval , poisson distribution , estimation , sampling (signal processing) , maximum likelihood , econometrics , computer science , management , filter (signal processing) , economics , computer vision
Summary Count data arising in various fields of applications are often under‐reported. Ignoring undercount naturally leads to biased estimators and inaccurate confidence intervals. In the presence of undercount, in this paper, we develop likelihood‐based methodologies for estimation of mean using validation data. The asymptotic distributions of the competing estimators of the mean are derived. The impact of ignoring undercount on the coverage and length of the confidence intervals is investigated using extensive numerical studies. Finally an analysis of heat mortality data is presented.