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A Cellular Genetic Algorithm with Disturbances: Optimisation - download pdf or read online

By Kirley M.

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Additional resources for A Cellular Genetic Algorithm with Disturbances: Optimisation Using Dynamic Spatial Interactions

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The first approach, described in the next section, develops the estimating equation and associated variance estimator for what might be called a full information maximum likelihood approach. That is, the likelihood is defined by the probability of observing all the relevant data available to the survey analyst. 3, develops the maximum sample likelihood estimator. 14 INTRODUCTION TO PART A This estimator maximises the likelihood defined by the sample data only, excluding population information. 4), where the unobservable population-level likelihood of interest is estimated using methods for descriptive inference.

Example 1 Consider the situation where Z is univariate and Y is bivariate, with components Y and X, and where Y, X and Z are independently and identically distributed as N(m, Æ) over the population of interest. We assume m0 ˆ (mY , mX , mZ ) is unknown but P Q sYY sYX sYZ Æ ˆ R sXY sXX sXZ S sZY sZY sZZ is known. Suppose further that there is full response and sampling is noninformative, so we can ignore iU and rU when defining the population likelihood. That is, in this case the survey data consist of the sample values of Y and X and the population values of Z, and g ˆ m.

On the other hand, the model expectation of the design-based variance is given by MORE COMPLEX ESTIMATORS ! N 2v N22 v2U Ex varp (^ b) ˆ Ex 12 1U N n1 N 2 n2  2  N1 N22 s2 ! X ˆ s2 2 2 N n1 N n2 n 37 (3X34) Thus, when the model is true and when the sampling fractions in the two strata are unequal, the design-based mean squared error of b^ is expected to be smaller than the design-based variance of ^ b. Example 3 illustrates that when the model holds, b^ may be better than ^b as an estimator of b, from the point of view of having the smaller design-based mean squared error.

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A Cellular Genetic Algorithm with Disturbances: Optimisation Using Dynamic Spatial Interactions by Kirley M.


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