On Sufficient Dimension Reduction Via Asymmetric Least Squares

On Sufficient Dimension Reduction Via Asymmetric Least Squares

Accompanying the advances in computer technology is an increase collection of high dimensional data in many scientific and social studies. Sufficient dimension reduction (SDR) is a statistical method that enable us to reduce the dimension ofpredictors without loss of regression information. In this dissertation, we introduce principal asymmetric least squares (PALS) as a unified framework for linear and nonlinear sufficient dimension reduction. Classical methods such as sliced inverse regression (Li, 1991) and principal support vector machines (Li, Artemiou and Li, 2011) often do not perform well in the presence of heteroscedastic error, while our proposal addresses this limitation by synthesizing different expectile levels. Through extensive numerical studies, we demonstrate the superior performance of PALS in terms of both computation time and estimation accuracy. For the asymptotic analysis of PALS for linear sufficient dimension reduction, we develop new tools to compute the derivative of an expectation of a non-Lipschitz function. PALS is not designed to handle symmetric link function between the response and the predictors. As a remedy, we develop expectile-assisted inverse regression estimation (EA-IRE) as a unified framework for moment-based inverse regression. We propose to first estimate the expectiles through kernel expectile regression, and then carry out dimension reduction based on random projections of the regression expectiles. Several popular inverse regression methods in the literature including slice inverse regression, slice average variance estimation, and directional regression are extended under this general framework. The proposed expectile-assisted methods outperform existing moment-based dimension reduction methods in both numerical studies and an analysis of the Big Mac data.

Imaging of Rheumatology, An Issue of Radiologic Clinics of North America

This issue of Radiologic Clinics of North America focuses on Imaging of Rheumatology, and is edited by Dr. Giuseppe Guglielmi. Articles will include: What the Rheumatologist is Looking For and What the Radiologist Should Know; Conventional Radiology in Rheumatoid Arthritis; Conventional Radiology in Spondyloarthritis; Conventional Radiology in Crystal Arthritis: Gout, Calcium Pyrophosphate Deposition, and Basic Calcium Phosphate Crystals; Ultrasound in Arthritis; Computed Tomography and Magnetic Resonance Imaging in Rheumatoid Arthritis; Computed Tomography and Magnetic Resonance Imaging in Spondyloarthritis; Computed Tomography and Magnetic Resonance Imaging in Crystal Arthritis; SAPHO and Recurrent Multifocal Osteomyelitis; Paediatric Vasculitis; Myopathies; Juvenile Arthritis and Other Pediatric Rheumatologic Disorders; Imaging of Post-Traumatic Arthritis, Aseptic Necrosis, Septic Arthritis, Sudek's Osteodystrophy, and Cancer Mimicking Arthritis; Imaging in Osteoarthritis; Interventions and Therapy in Rheumatology, and more!

Japanese Science and Technology, 1983-1984