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Asymptotic Confidence Intervals for Parameters Estimated through the Ratio of Asymptotically Normal Statistics

digital Asymptotic Confidence Intervals for Parameters Estimated
through the Ratio of Asymptotically Normal Statistics
Article
journal STATISTICA & APPLICAZIONI
issue STATISTICA & APPLICAZIONI - 2019 - 1
title Asymptotic Confidence Intervals for Parameters Estimated through the Ratio of Asymptotically Normal Statistics
authors

publisher Vita e Pensiero
format Article | Pdf
online since 08-2020
doi 10.26350/999999_000017
issn 18246672 (print)
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In this paper, four different approaches for the definition of asymptotic confidence intervals for the ratio of two unknown parameters are reviewed and compared via a simulation study. The considered approaches are based on the well known Delta Method and on the distribution of the ratio of correlated normal random variables. Simulations concern the ratio between two expectations, the Coefficient of Variation, the Gini Concentration Ratio, and the Sharpe Ratio. It is shown that the asymptotic confidence intervals based on the ratio of correlated normal random variables often have a better coverage accuracy with respect to the ones derived from Delta Method, even if the observed gain is small in some cases.

keywords

ratio of correlated normal random variables, Delta Method, Gini Concentration Ratio, Coefficient of Variation, Sharpe Ratio.

Authors biography

Dipartimento di Statistica e Metodi Quantitativi - Universita` degli studi di Milano-Bicocca, via Bicocca degli Arcimboldi, 8, 20126 MILANO (e-mail:lucio.decapitani1@unimib.it; marcella.mazzoleni@unimib.it; angiola.pollastri@unimib.it).