# New Research

2008/01/01

# The World of Statistical Analysis

## ---- Nonlinear and Robust Statistical Procedures ----

### Prof. Shingo SHIRAHATA, Associate Prof. Wataru SAKAMOTO, Assistant Prof. Mie FUJIKI

The Shirahata Laboratory (Statistical Analysis Group) studies how to analyze statistical data with errors, fluctuations or individual variations. Almost all observations appeared in natural science, engineering science, medical science, social science and human science are contaminated by errors and hence they do not show their truth. We are developing methodologies to reveal the true features by removing the errors. The approaches to attack the problems are to construct new models and statistical procedures and to study their mathematical and statistical properties.

Statistical methodologies are, at first, developed for linear statistical inferences. At present, as the fields with data to be analyzed are expanded, statistical data to be analyzed have more complex structure. Hence classical statistical procedures are hard to apply and it is required to develop new methodologies. Both computer hardware and software technologies have made rapid progress recently. Therefore, it becomes possible to apply several procedures which are known to have good properties but were difficult to apply due to their hard task of computation. Further, the studies on nonparametric procedures which require only weak assumptions on the models are becoming active. Computer intensive methods like bootstrap procedures which are developed under the premise of existence of computers are also becoming active.

At Shirahata Laboratory we are studying on the following problems.

(1). Smoothing methods, theory and applications. The smoothing methods are required to remove error terms included in the observations and to obtain the main terms.

(2). Analysis on the data with very complex structures and development how to perform experiments. For example, medical data obtained in order to measure the effects of new medicine include several covariates such as sex, age, extent of illness and so on and have very complex structures. Hence we need to construct efficient experiments.

(3). Robust procedures. Many statistical procedures are applied under some assumptions. If the assumptions are strong, we can construct very effective procedures when they are the cases. However, such procedures lose validity when the assumptions are not true. Thus, we need robust procedures which have high efficiency when the standard assumptions are not true.

The staffs of the laboratory are working as president, councilor or director of Japanese Society of Computational Statistics. In this year we shall have world conference of International Association of Statistical Computing. We are at work to make the conference successful. Further some members are making efforts to propagate medical statistics as central members of an NPO (Biostatistics Research Association).