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In decision theory, a decision rule is a function which maps an observation to an appropriate action. Decision rules play an important role in the theory of statistics and economics , and are closely related to the concept of a strategy in game theory .
In statistical decision theory, a randomised decision rule or mixed decision rule is a decision rule that associates probabilities with deterministic decision rules. In finite decision problems, randomised decision rules define a risk set which is the convex hull of the risk points of the nonrandomised decision rules.
Stein's example is surprising, since the "ordinary" decision rule is intuitive and commonly used. In fact, numerous methods for estimator construction, including maximum likelihood estimation, best linear unbiased estimation, least squares estimation and optimal equivariant estimation, all result in the "ordinary" estimator.
The mythological judgement of Paris required selecting from three incomparable alternatives (the goddesses shown).. Decision theory or the theory of rational choice is a branch of probability, economics, and analytic philosophy that uses the tools of expected utility and probability to model how individuals would behave rationally under uncertainty.
An estimator or decision rule with zero bias is called unbiased. In statistics, "bias" is an objective property of an estimator. Bias is a distinct concept from consistency : consistent estimators converge in probability to the true value of the parameter, but may be biased or unbiased (see bias versus consistency for more).
In decision theory, a decision rule is said to dominate another if the performance of the former is sometimes better, and never worse, than that of the latter. Formally, let δ 1 {\displaystyle \delta _{1}} and δ 2 {\displaystyle \delta _{2}} be two decision rules , and let R ( θ , δ ) {\displaystyle R(\theta ,\delta )} be the risk of rule ...
A decision rule that minimizes (,) is called a Bayes rule with respect to (). There may be more than one such Bayes rule. There may be more than one such Bayes rule. If the Bayes risk is infinite for all δ {\displaystyle \delta \,\!} , then no Bayes rule is defined.
The weighted average rule gives different weights to different voters (for example, based on their level of expertise). The trimmed average rule discards some of the extreme bids, and returns the average of the remaining bids. Renault and Trannoy study the combined use of the average rule and the majority rule, and their effect on minority ...