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We propose a nonparametric method to test which characteristics provide independent 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 is insensitive to outliers. Many of the previously identified return predictors do not provide incremental information for expected returns, and nonlinearities are important. Our proposed method has higher out-of-sample explanatory power compared to linear panel regressions, and increases Sharpe ratios by 50%.