Abstract
This paper provides an asymptotic expansion for the distribution of the Studentized linear discriminant function with -step monotone missing training data. It turns out to be a certain generalization of the results derived by Anderson [1] and Shutoh and Seo [12]. Furthermore we also derive the cut-off point constrained by a conditional probability of misclassification using the idea of McLachlan [8]. Finally we perform Monte Carlo simulation to evaluate our results.
Funding Statement
This research was in part supported by grants from the Forum for Asian Studies (4440101-2010), Stockholm University, Sweden. N. Shutoh’s and M. Hyodo’s research was in part supported by Grant-in-Aid for JSPS Fellows (23·6926, 23·9731). T. Pavlenko’s research was in part supported by grants from Swedish Research Council (421-2008-1966). T. Seo’s research was in part supported by Grant-in-Aid for Scientific Research (C) (23500360).
Acknowledgements
The authors would like to extend their sincere gratitude to the Editor and the referee who gave invaluable comments and suggestions, which have greatly enhanced this paper. Any remaining errors are the authors’ responsibility.
Citation
Nobumichi Shutoh. Masashi Hyodo. Tatjana Pavlenko. Takashi Seo. "Constrained linear discriminant rule via the Studentized classification statistic based on monotone missing data." SUT J. Math. 48 (1) 55 - 69, January 2012. https://doi.org/10.55937/sut/1345734342
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