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

digital

Article

Magazine

STATISTICA & APPLICAZIONI

Section

Open Access

Title

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

Authors

Lucio De Capitani, Marcella Mazzoleni, Angiola Pollastri

Publisher

Vita e Pensiero

Format

Article |

Pdf

Online from

08-2020

Doi

10.26350/999999_000017

Issn

1824-6672 (print) | 2283-6659 (digital)

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Description Readers' comments

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).

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