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A function used to quantify the difference between observed data and predicted values according to a model. Minimization of loss functions is a way to estimate the parameters of the model.

Examples include:

  • The (Root) Mean Squared Error, , used in "ordinary" regression or ordinary (OLS)
  • The Mean Absolute Error, , frequently used in forecasting
  • "Hinge" losses, or linear losses where over- and underpredictions are weighted differently, for
  • (Proper) , used to compare predictive densities to actuals