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Selecting these n h optimally can be done in various ways, using (for example) Neyman's optimal allocation. There are many reasons to use stratified sampling: [7] to decrease variances of sample estimates, to use partly non-random methods, or to study strata individually. A useful, partly non-random method would be to sample individuals where ...
Optimum allocation (or disproportionate allocation) – The sampling fraction of each stratum is proportionate to both the proportion (as above) and the standard deviation of the distribution of the variable. Larger samples are taken in the strata with the greatest variability to generate the least possible overall sampling variance.
In Computer Science, Optimal Computing Budget Allocation (OCBA) is a simulation optimization method designed to maximize the Probability of Correct Selection (PCS) while minimizing computational costs. First introduced by Dr. Chun-Hung Chen in the mid-1990s, OCBA determines how many simulation runs (or how much computational time) or the number ...
The envelope theorem describes how the value of an optimal solution changes when an underlying parameter changes. The process of computing this change is called comparative statics. The maximum theorem of Claude Berge (1963) describes the continuity of an optimal solution as a function of underlying parameters.
Somewhat surprisingly for an optimal control problem, a closed-form solution exists. The optimal consumption and stock allocation depend on wealth and time as follows: [4]: 401 (,) =. This expression is commonly referred to as Merton's fraction.
Stratified sampling can yield that is smaller than 1 when using Proportionate allocation to strata sizes (when these are known a-priori, and correlated to the outcome of interest) or Optimum allocation (when the variance differs between strata and is known a-priori). [citation needed]
The algorithm also is designed for two parties only; when there are three or more parties, there may be no allocation that is simultaneously envy-free, equitable, and Pareto-optimal. This can be shown by the following example, constructed by J.H.Reijnierse, [2]: 82–83 involving three parties and their valuations: Alice: 40, 50, 10
A significant aspect of the Pareto frontier in economics is that, at a Pareto-efficient allocation, the marginal rate of substitution is the same for all consumers. [5] A formal statement can be derived by considering a system with m consumers and n goods, and a utility function of each consumer as = where = (,, …,) is the vector of goods, both for all i.