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.

de Capitani, L., Mazzoleni, M., Pollastri, A. (2019). Asymptotic confidence intervals for parameters estimated through the ratio of asymptotically normal statistics. STATISTICA & APPLICAZIONI, 17(1), 3-33 [10.26350/999999_000017].

Asymptotic confidence intervals for parameters estimated through the ratio of asymptotically normal statistics

de Capitani L.;Mazzoleni M.;Pollastri A.
2019

Abstract

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.
Articolo in rivista - Articolo scientifico
Coefficient of Variation; Delta Method; Gini Concentration Ratio; Ratio of correlated normal random variables; Sharpe Ratio;
English
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33
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de Capitani, L., Mazzoleni, M., Pollastri, A. (2019). Asymptotic confidence intervals for parameters estimated through the ratio of asymptotically normal statistics. STATISTICA & APPLICAZIONI, 17(1), 3-33 [10.26350/999999_000017].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/350351
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