New developments of theories in multivariate statistical inference and their applications

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In this research project, new procedures were derived in estimation, hypothesis testing, predction and variable selection in multivariate statistical models as well as theories for justfying the new procedures were developed. In particular, we treated problems, models or situations where conventional methods had drawbacks for use or were not available, and then we tried to derive and suggest procedures which could resolve the problems. Of these, the following multivatiate statistical issues were addressed and new theories were developed with applications: (1) higher order asymptotic corrections in mean squared errors and confidence intervals in small area estimation, (2) benchmark problems in small area estimation under continuous and discrete mixed models, (3) Bartlett corrections and methods for variable selection in linear mixed models, (4) high dimensional procedures in linear discrimination and (5) optimality in estimation of multi-dimensional parameters.