The frequentist procedures of significance testing and confidence intervals can be constructed without regard to utility functions. However, some elements of frequentist statistics, such as statistical decision theory, do incorporate utility functions. In particular, frequentist developments of optimal inference (such as minimum-variance unbiased estimators, or uniformly most powerful testing) make use of loss functions, which play the role of (negative) utility functions. Loss functions need not be explicitly stated for statistical theorists to prove that a statistical procedure has an optimality property.Preface to Pfanzagl. However, loss-functions are often useful for stating optimality properties: for example, median-unbiased estimators are optimal under absolute value loss functions, in that they minimize expected loss, and least squares estimators are optimal under squared error loss functions, in that they minimize expected loss.
the frequentist procedures of significance testing and confidence intervals can be constructed without regard to utility functions however some elements of frequentist statistics such as statistical decision theory do incorporate utility functions in particular frequentist developments of optimal inference (such as minimum-variance unbiased estimators or uniformly most powerful testing) make use of loss functions which play the role of (negative) utility functions loss functions need not be explicitly stated for statistical theorists to prove that a statistical procedure has an optimality propertypreface to pfanzagl however loss-functions are often useful for stating optimality properties for example median-unbiased estimators are optimal under absolute value loss functions in that they minimize expected loss and least squares estimators are optimal under squared error loss functions in that they minimize expected loss