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.
ratio of correlated normal random variables, Delta Method, Gini Concentration Ratio,
Coefficient of Variation, Sharpe Ratio.
Biografia degli autori
Dipartimento di Statistica e Metodi Quantitativi - Universita` degli studi di Milano-Bicocca, via Bicocca degli Arcimboldi, 8, 20126 MILANO (e-mail:firstname.lastname@example.org; email@example.com; firstname.lastname@example.org).