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Efficiency is very often confused with effectiveness. In general, efficiency is a measurable concept, quantitatively determined by the ratio of useful output to total useful input. Effectiveness is the simpler concept of being able to achieve a desired result, which can be expressed quantitatively but does not usually require more complicated ...
For example, if a distribution is a combination of 98% N(μ, σ) and 2% N(μ, 10σ), the presence of extreme values from the latter distribution (often "contaminating outliers") significantly reduces the efficiency of the sample mean as an estimator of μ.
The efficiency ratio indicates the expenses as a percentage of revenue (expenses / revenue), with a few variations – it is essentially how much a corporation or individual spends to make a dollar; entities are supposed to attempt minimizing efficiency ratios (reducing expenses and increasing earnings). The concept typically applies to banks.
An inadmissible rule is not preferred (except for reasons of simplicity or computational efficiency), since by definition there is some other rule that will achieve equal or lower risk for all. But just because a rule δ {\displaystyle \delta \,\!} is admissible does not mean it is a good rule to use.
Since the idea is about pure mathematics and logic, similar arguments abound much further afield. They, for example, lead to the necessity of the fifth normal form in relational database design. The history of the argument also goes deeper, Condorcet's paradox perhaps being the first example of the finite sort.
Designs can be optimized when the design-space is constrained, for example, when the mathematical process-space contains factor-settings that are practically infeasible (e.g. due to safety concerns). Minimizing the variance of estimators
For example, if the variance of a random variable is said to be finite, this implies it is a non-negative real number, possibly zero. In some contexts though, for example in "a small but finite amplitude", zero and infinitesimals are meant to be excluded.
In computer science, algorithmic efficiency is a property of an algorithm which relates to the amount of computational resources used by the algorithm. Algorithmic efficiency can be thought of as analogous to engineering productivity for a repeating or continuous process. For maximum efficiency it is desirable to minimize resource usage.