3.4. * Loss Function and Decision#

Warning

This learning outcome is considered optional in [OhioDoHEducation21]. We include it here but do not develop it.

Learning Outcome

Formulate statistical inference as a decision problem, specify a generative statistical model, a target of inference, and a loss function, and then select an estimator by minimization of average loss over simulated data sets.

Sample Tasks

  • Choose among mean, median, and trimmed mean as an estimator in a simple model, when the target is the center of the distribution and the loss function is squared error loss. (Note that the choice will depend on the generative model).

  • Understand 0-1 loss for a two-choice problem.

  • Demonstrate that the loss function determines the target of estimation (e.g., estimation of a quantile can be accomplished by minimization of an asymmetric absolute error loss function).

  • Make use of squared error predictive loss in a simple linear regression setting.

  • Design a loss function for a problem of the student’s choosing.

[OhioDoHEducation21]