Michael Woodroofe Lecture Series: Cun-Hui Zhang, Distinguished Professor, Department of Statistics and Biostatistics, Rutgers University
"Multiple Isotonic Regression and Power-One Test for Higher Criticism"
We consider two problems in areas to which Michael Woodroofe has made seminal contributions. In multiple isotonic regression, a block estimator is developed to attain minimax rate for a wide range of signal-to-noise ratio, to achieve adaptation to the parametric root-n rate up to a logarithmic factor in the case where the unknown mean is piecewise constant, and to achieve variable selection consistency. In higher criticism, we develop a one-sided sequential probability ratio test based on the ordered p-values to achieve optimal detection of rare and weak signals. This makes an interesting connection to the test of power one. Nonlinear renewal theorem is used to approximate the size of the test.
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