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Despite the widespread application of statistical downscaling tools, uncertainty remains regarding the role of model formulation in determining model skill for daily maximum and minimum temperature (T_maxandT_min), and precipitation occurrence and intensity. Impacts of several key aspects of statistical transfer function form on model skill are evaluated using a framework resistant to model overspecification. We focus on: (a) model structure: simple (generalized linear models, GLMs) versus complex (artificial neural networks, ANNs) models. (b) Predictor selection: Fixed number of predictors chosena prioriversus stepwise selection of predictors and inclusion of grid point values versus predictors derived from application of principal components analysis (PCA) to spatial fields. We also examine the influence of domain size on model performance. For precipitation downscaling, we consider the role of the threshold used to characterize a wet day and apply three approaches (Poisson and Gamma distributions in GLM and ANN) to downscale wet‐day precipitation amounts. While no downscaling formulation is optimal for all predictands and at 10 locations representing diverse U.S. climates, and due to the exclusion of variance inflation all of the downscaling formulations fail to reproduce the range of observed variability, models with larger suites of prospective predictors generally have higher skill. For temperature downscaling, ANNs generally outperform GLM, with greater improvements forT_minthanT_max. Use of PCA‐derived predictors does not systematically improve model skill, but does improve skill for temperature extremes. Model skill for precipitation occurrence generally increases as the wet‐day threshold increases and models using PCA‐derived predictors tend to outperform those based on grid cell predictors. Each model for wet‐day precipitation intensity overestimates annual total precipitation and underestimates the proportion derived from extreme precipitation events, but ANN‐based models and those with larger predictor suites tend to have the smallest bias.