Estimation of and inference on a vector of proportions, with jointly increasing population and sample size

  • This paper proposes a method for deriving the joint asymptotic distribution of sample proportions when the population and sample size increase jointly to infinity. The joint distribution of the sample proportions is derived by reducing the multi- variate to a univariate problem and applying the Cramer-Wold device. Knowing the asymptotic distribution we are in a position to conduct inference on linear or non-linear functions of the population proportions such as a ratio or the log-odds. We motivate and develop our method by means of a topical epidemiological application, namely the infection fatality rate of a virus such as SARS-CoV-2. We demonstrate that our method can be extended to more general settings of interest.

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Author:Norbert Christopeit, Michael Massmann
Series (Serial Number):WHU – Working Paper Series in Economics (WP 21/01)
Publisher:WHU - Otto Beisheim School of Management
Place of publication:Vallendar
Document Type:Working Paper
Date of Publication (online):2021/08/30
Date of first Publication:2021/08/30
Publishing Institution:WHU - Otto Beisheim School of Management
Release Date:2021/08/30
Tag:Cramér-Wold device; Finite population correction; Infection fatality rate; Joint asymptotics; Ratio of proportions; Simultaneous inference
Page Number:24
Institutes:WHU Economics Group / Chair of Econometrics and Statistics
Licence (German):Copyright for this publication