Yuzo Maruyama is Professor of Statistics at Kobe University. He earned his M.S. and Ph.D. degrees, both in Economics, at the University of Tokyo. His research interests include statistical decision theory, shrinkage estimation, and Bayesian model selection.Tatsuya Kubokawa is Professor in the Faculty of Economics at the University of Tokyo. He earned his M.S. and Ph.D. degrees, both in Mathematics, at University of Tsukuba. His research interests include statistical decision theory, multivariate analysis, and mixed-effects modeling.William E. Strawderman is Professor of Statistics at Rutgers University. He earned an M.S. in Mathematics from Cornell University and a second M.S. in Statistics from Rutgers and then completed his Ph.D. in Statistics, also at Rutgers. He is Fellow of both the Institute of Mathematical Statistics and American Statistical Society and Elected Member at International Statistical Institute. His research interests include statistical decision theory, shrinkage estimation, and Bayesian statistics.

• 1. Decision Theory Preliminaries.- 2. Minimaxity and Improvement on the James-Stein estimator.- 3. Admissibility.

Yuzo Maruyama is Professor of Statistics at Kobe University. He earned his M.S. and Ph.D. degrees, both in Economics, at the University of Tokyo. His research interests include statistical decision theory, shrinkage estimation, and Bayesian model selection.Tatsuya Kubokawa is Professor in the Faculty of Economics at the University of Tokyo. He earned his M.S. and Ph.D. degrees, both in Mathematics, at University of Tsukuba. His research interests include statistical decision theory, multivariate analysis, and mixed-effects modeling.William E. Strawderman is Professor of Statistics at Rutgers University. He earned an M.S. in Mathematics from Cornell University and a second M.S. in Statistics from Rutgers and then completed his Ph.D. in Statistics, also at Rutgers. He is Fellow of both the Institute of Mathematical Statistics and American Statistical Society and Elected Member at International Statistical Institute. His research interests include statistical decision theory, shrinkage estimation, and Bayesian statistics.

• 1. Decision Theory Preliminaries.- 2. Minimaxity and Improvement on the James-Stein estimator.- 3. Admissibility.

Yuzo Maruyama is Professor of Statistics at Kobe University. He earned his M.S. and Ph.D. degrees, both in Economics, at the University of Tokyo. His research interests include statistical decision theory, shrinkage estimation, and Bayesian model selection.Tatsuya Kubokawa is Professor in the Faculty of Economics at the University of Tokyo. He earned his M.S. and Ph.D. degrees, both in Mathematics, at University of Tsukuba. His research interests include statistical decision theory, multivariate analysis, and mixed-effects modeling.William E. Strawderman is Professor of Statistics at Rutgers University. He earned an M.S. in Mathematics from Cornell University and a second M.S. in Statistics from Rutgers and then completed his Ph.D. in Statistics, also at Rutgers. He is Fellow of both the Institute of Mathematical Statistics and American Statistical Society and Elected Member at International Statistical Institute. His research interests include statistical decision theory, shrinkage estimation, and Bayesian statistics.

• 1. Decision Theory Preliminaries.- 2. Minimaxity and Improvement on the James-Stein estimator.- 3. Admissibility.