Non-parametric confidence intervals for covariance and correlation

Consider a sample of independent and identical bivariate observations. Simple consistent confidence intervals for the variances, covariance, and correlation of the underlying population are obtained from their influence functions. They contrast with their confidence intervals obtained under the assumption of normality, which are shown to be not consistent if the assumption of normality is false. Even when the marginals are normal, we show that Fisher’s <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$z$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>z</mi> </math> </EquationSource> </InlineEquation>-transformation may be quite inappropriate. Copyright Sapienza Università di Roma 2014