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Major Research Subjects of Maruyama, Y. (2001-) Associate Professor
Further information is available at http://www.csis.u-tokyo.ac.jp/~maruyama/
- Research on Statistical Decision Theory
In the field of statistical estimation with small sample, usual
procedures such as unbiased or maximum likelihood estimators,
sometimes have drawbacks of instability or inefficiency. Also
they sometimes take undesirable values beyond the parameter spaces.
This phenominon is called the Stein one and have fascinated many
statisticans for a long time. But almost all results on the phenomin
have been derived on the assumption that the distribution is multivariate
normal. We have investigated the Stein phenomenon under the normality
thoroughly, and have also studied it in the non-normal case. Recently
I derived a generalized Bayes estimator with several good properties
in non-normal case.
- Research on Small Area Estimation
Small Area Estimation is a practical problem which has been paid
attention to especially by Census Bureau of various countries.
It is needed in the following reason. If, in a survey sampling,
we are interested in estimating not the population mean of the
whole area but the population mean of a certain small area, the
sample mean of a certain small area is often unstable and has
a large standard error because of smallness of sampling size.
A simple idea for eliminating the drawback is a suitable insertion
of sampling data of some areas next to a certain area. I would
like to derive some good estimators using our research on statistical
decision theory.
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