Quadratic Loss Function
The use of a quadratic loss function is common, for example when using least squares techniques or Taguchi methods. It is often more mathematically tractable than other loss functions because of the properties of variances, as well as being symmetric: an error above the target causes the same loss as the same magnitude of error below the target. If the target is t, then a quadratic loss function is
for some constant C; the value of the constant makes no difference to a decision, and can be ignored by setting it equal to 1.
Many common statistics, including t-tests, regression models, design of experiments, and much else, use least squares methods applied using linear regression theory, which is based on the quadratric loss function.
The quadratic loss function is also used in linear-quadratic optimal control problems.
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