In this paper, assuming that returns follows a stationary and ergodic stochastic process, the asymptotic distribution of the natural estimator of the Sharpe Ratio is explicitly given. This distribution is used in order to define an approximated confidence interval for the Sharpe ratio. Particular attention is devoted to the case of the GARCH(1,1) process. In this latter case, a simulation study...

Point estimates of unknown parameters θ governing the distribution of an observed quantity X are unsatisfying if they come with no measure of accuracy or precision. One approach to giving such a measure is to offer interval estimates for θ, rather than point estimates; upon observing X, we construct an interval [a, b] which is very likely to contain θ, and which is very short. The approach to e...

Methodological recommendations strongly emphasize the routine reporting of effect sizes and associated confidence intervals to express the uncertainty around the primary outcomes. Confidence intervals (CI) for unstandardized effects are easy to construct; However, CI’s for standardized measures such as the standardized mean difference (i.e., Cohen’s d), the Pearson product-moment correlation, p...

The confidence interval, its close cousin the p-value, and other statistical summaries of data are widely used in science, including the occupational and environmental health sciences, but they are almost as widely misused. My purpose here is to review some basic matters that should be covered in every introductory statistics course, but are generally omitted. More specifically, some of the man...