Standard regression models within the broad class of ‘generalised linear models’ require the specification of a family of distribution functions.  Diagnostic tests are performed to see if the residuals follow a distribution consistent with the chosen model form.  In this project we examine regression models with a residual distribution that adapts to the data via a kernel-density estimator.  The goal of the project is to develop an estimation method applicable to regression problems that does not require specification of a parametric error distribution.