We provide a nonparametric revealed preference approach to demand analysis based on homothetic efficiency. Homotheticity is a useful restriction but data rarely satisfies testable conditions. To overcome this we provide a way to estimate homothetic efficiency of consumption choices. It generalises Heufer's (2013) two-dimensional concept to arbitrary dimensions and is motivated by a form of rationalisation similar to Halevy et al. (2012). The method allows to recover larger preferred and worse sets and provides considerably more preditive success and discriminatory power against random behaviour. An application to experimental and household expenditure data illustrates the potential of our approach.