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Based on asymptotic approximations we provide explicit formulas for the proposed sampling plans and an effective recursive algorithm for their calculation.
This procedure produced somewhat wider confidence intervals than those based on asymptotic approximations, so we report only the more conservative bootstrapped estimates.
This is not too surprising since mixed model test statistics are based on asymptotic approximations, and others [13], [14] have raised concerns about inflated type I error rates when using these tests.
Szpiro and his colleagues developed a method for measurement error correction based on asymptotic approximations that derived for linear regression for the exposure and health models [ 64, 65].
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The proposed variants of AIC are based on asymptotic approximation of bootstrap type estimates of Kullback Leibler information.
RR was estimated with the adjusted odds ratio (OR) derived from the multivariate logistic regression models and confidence intervals were based on asymptotic approximation [ 20].
Pseudo empirical likelihood ratio confidence intervals for finite population parameters are based on asymptotic χ2 approximation to an adjusted pseudo empirical likelihood ratio statistic, with the adjustment factor related to the design effect.
This approach, based on asymptotic expansion, gives the first-order approximation of the 3D elasticity problem from the solution of a 2D microscopic problem posed on the cross-section and a 1D macroscopic problem, which turns out to be a Navier Bernoulli Saint-Venant beam problem.
This is largely due to the fact that the analytical approximation is based on asymptotic analytical solution which ignores the stochastic effects due to the finite number of iterations.
Our method is particularly suited for traits with very low prevalence, where standard methods based on asymptotic theory become unreliable (the normal approximation works only with high information content and/or parameter values far removed from the boundaries of the parameter space).
For rare diseases, estimation methods based on asymptotic theory cannot be applied due to very low cell probabilities.
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