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Asymptotic expansion of the distribution of the studentized linear discriminant function with 2-Step monotone missing data

In discriminant analysis, it is important to evaluate probabilities of misclassification. Therefore some asymptotic approximations have been proposed in case that all the sample vectors do not have missing data. Also it is known that asymptotic expansions of the distribution of discriminant function are useful techniques for considering asymptotic approximation in sample vectors with small dimension. By using perturbation method, an extension for Anderson (1973) in the case of 2-Step monotone missing samples is given. Finally, numerical evaluations by Monte Carlo simulations are given.