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It has been shown that estimators using other variables' information provide more accurate estimation for θ than the intuitive estimator does [ 22].
An intuitive estimator of θ is Y (i.e. θ ^ i = Y i, i = 1, …, k ).
Note this is an intuitive estimator, as it just represents the mean value of g y) with respect to the available distances y.
However, Stein [ 22] showed that when k ≥ 3, there exists other estimators with smaller mean squared error than the intuitive estimator Y.
For k ≥ 3, under the squared error loss, the intuitive estimator Y is dominated by the estimator (2) θ ^ J S = 1 - k - 2 S Y 2 Y, where S Y 2 = ∑ i = 1 k Y i 2 [ 23].
In fact, except for the estimator in (3), the estimators of the form (4) θ ^ i J S = 1 - c S Y 2 Y i all have uniformly smaller mean squared error than the intuitive estimator Y i, for k ≥ 3 and 0 < c <2 (k - 2).
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This estimator has an intuitive appeal because it can be viewed as a Kaplan-Meier estimator computed on k components, one for each stratum, in which all the mj controls are given the same weight.
These estimates have intuitive interpretations.
These estimators are based on intuitive basic identities that were explicitly shown by Cockerham [ 8] (and also [ 9]), namely, that resemblance between genotypes is a function of coancestry (identity by descent) and allelic frequencies at the base population.
This index is considered the best estimator of sexual dimorphism because it is intuitive, linear, symmetrical, and directional [ 63].
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