We propose a nonparametric method to study which characteristics provide incremental information for the cross section of expected returns. We use the adaptive group LASSO to select characteristics and to estimate how they affect expected returns nonparametrically. Our method can handle a large number of characteristics, allows for a flexible functional form, and our implementation is insensitive to outliers. Many of the previously identified return predictors do not provide incremental information for expected returns, and nonlinearities are important. We study the properties of our method in an extensive simulation study and out-of-sample prediction exercise and find large improvements both in model selection and prediction compared to alternative selection methods. Our proposed method has higher out-of-sample Sharpe ratios and explanatory power compared to linear panel regressions.