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A decision rule is admissible (with respect to the loss function) if and only if no other rule dominates it; otherwise it is inadmissible. Thus an admissible decision rule is a maximal element with respect to the above partial order.
Nevertheless, admissibility of rules is known to be decidable in many modal and superintuitionistic logics. The first decision procedures for admissible rules in basic transitive modal logics were constructed by Rybakov, using the reduced form of rules. [12] A modal rule in variables p 0, ... , p k is called reduced if it has the form
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 ...
In a finite decision problem, the risk point of an admissible decision rule has either lower x-coordinates or y-coordinates than all other risk points or, more formally, it is the set of rules with risk points of the form (,) such that {(,):,} = (,). Thus the left side of the lower boundary of the risk set is the set of admissible decision rules.
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 .
Admissible decision rule, in statistical decision theory, a rule which is never dominated; Admissible rule, in logic, a type of rule of inference; Admissible heuristic, in computer science, is a heuristic which is no more than the lowest-cost path to the goal; Admissible prime k-tuple, in number theory regarding possible constellations of prime ...
These rules are often inadmissible and the verification of their admissibility can be difficult. For example, the generalized Bayes estimator of a location parameter θ based on Gaussian samples (described in the "Generalized Bayes estimator" section above) is inadmissible for p > 2 {\displaystyle p>2} ; this is known as Stein's phenomenon .
The parameter space has just two elements and each point on the graph corresponds to the risk of a decision rule: the x-coordinate is the risk when the parameter is and the y-coordinate is the risk when the parameter is . In this decision problem, the minimax estimator lies on a line segment connecting two deterministic estimators.