In statistics, decision theory and economics, a loss function is a function that maps an event (technically an element of a sample space) onto a real number representing the economic cost or regret associated with the event.

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  • In statistics, decision theory and economics, a loss function is a function that maps an event (technically an element of a sample space) onto a real number representing the economic cost or regret associated with the event. Less technically, in statistics a loss function represents the loss (cost in money or loss in utility in some other sense) associated with an estimate being "wrong" (different from either a desired or a true value) as a function of a measure of the degree of wrongness (generally the difference between the estimated value and the true or desired value.) Both Frequentist and Bayesian statistical theory involve calculating statistics in such a way as to minimize the expected loss observed from being wrong given a set of assumptions about the data and ones loss function. Sound statistical practice requires selecting an estimator consistent with the actual loss experienced in the context of a particular applied problem. Thus, in the applied use of loss functions, selecting which statistical method to use to model an applied problem depends on knowing the losses that will be experienced from being wrong under the problem's particular circumstances, which results in the introduction of an element of teleology into problems of scientific decision-making . A common example involves estimating "location". Under typical statistical assumptions, the mean or average is the statistic for estimating location that minimizes the expected loss experienced under the Taguchi or squared-error loss function, while the median is the estimator that minimizes expected loss experienced under the absolute-difference loss function. Still different estimators would be optimal under other, less common circumstances. Loss functions in economics are typically expressed in monetary terms. For example: : \$ = \frac{\mathrm{loss}}{\mathrm{time\ period}}. Other measures of cost are possible, for example mortality or morbidity in the field of public health or safety engineering. Loss functions are complementary to utility functions which represent benefit and satisfaction. Typically, for utility U: :\ \mathrm{loss} = f(k - U) where k is some arbitrary constant. (en)
  • En estadística, teoría de la decisión y economía, una función de pérdida es una función que relaciona un evento (técnicamente un elemento de un espacio de muestreo) con un número real que representa el coste económico asociado con el evento. Las funciones de pérdida en economía se expresan normalmente en términos monetarios. Por ejemplo: :\ $ = \frac{\mathrm{perdida}}{\mathrm{tiempo}} Son posibles otras medidas del coste, por ejemplo mortalidad o morbilidad en el campo de la salud pública o ingeniería de seguridad. Las funciones de pérdida son complementarias de las funciones de utilidad que representan beneficio y satisfacción. Típicamente, para utilidad U: :\ \mathrm{perdida} = k - U donde k es una constante arbitraria. (es)
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  • In statistics, decision theory and economics, a loss function is a function that maps an event (technically an element of a sample space) onto a real number representing the economic cost or regret associated with the event. (en)
  • En estadística, teoría de la decisión y economía, una función de pérdida es una función que relaciona un evento (técnicamente un elemento de un espacio de muestreo) con un número real que representa el coste económico asociado con el evento. (es)
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  • Loss function (en)
  • Función de pérdida (es)
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