Summary: Estimation of a relative risk function using a ratio of two kernel density estimates is considered, concentrating on the problem of choosing the smoothing parameters. A cross-validation method is proposed, compared with a range of other methods and found to be an improvement when the actual risk is close to constant. In particular, theoretical and empirical comparisons demonstrate the advantage of choosing the smoothing parameters jointly. The methodology was motivated by a class of problems in environmental epidemiology, and an application in this area is described.