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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.
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 ...
Example of the optimal Kelly betting fraction, versus expected return of other fractional bets. In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a sequence of bets by maximizing the long-term expected value of the logarithm of wealth, which is equivalent to maximizing the long-term expected geometric growth rate.
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]
Optimal designs offer three advantages over sub-optimal experimental designs: [5] Optimal designs reduce the costs of experimentation by allowing statistical models to be estimated with fewer experimental runs. Optimal designs can accommodate multiple types of factors, such as process, mixture, and discrete factors.
Portfolio optimization is the process of selecting an optimal portfolio (asset distribution), out of a set of considered portfolios, according to some objective.The objective typically maximizes factors such as expected return, and minimizes costs like financial risk, resulting in a multi-objective optimization problem.
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