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The hybrid method of FSIR and FSAVE for functional effective dimension reduction
Affiliation:1. College of Economics, Jinan University, Guangzhou, 510632, China;2. Institute of Statistical Sciences, College of Mathematics and Computational Science, Shenzhen University, Shenzhen, 518060, China;3. Department of Statistics, The Chinese University of Hong Kong, Hong Kong;4. College of Statistics, Capital University of Economics and Business, Beijing, 100070, China;1. Department of Statistics, DB Parumala College, Pampa- 689 626, India;2. Department of Statistics, University of Kerala, Thiruvananthapuram- 695 581, India;1. Department of Genitourinary Oncology, Moffitt Cancer Center, Tampa, FL;2. Department of Biostatistics, Moffitt Cancer Center, Tampa, FL;1. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, China;2. School of Mathematics & Physics, Anhui Polytechnic University, Wuhu, China;3. Research Center of Applied Statistics and Institute of Statistics and Big Data, Renmin University of China, China;1. Department of Internal Medicine, University of Manitoba, Winnipeg, MB, Canada;2. Department of Medicine, McGill University, Montreal, QC, Canada;3. Department of Medicine, Memorial University, St. John''s, NL, Canada;4. Department of Medicine, University British Columbia, Vancouver, BC, Canada;5. Department of Medicine, University of Toronto, Toronto, ON, Canada;6. Department of Medicine, University of Saskatchewan, Saskatoon, SK, Canada;7. Department of Medicine, Queen''s University, Kingston, ON, Canada;8. Departments of Medicine, Oncology, and Community Health Sciences, University of Calgary, Calgary, AB, Canada;9. Division of Endocrinology and Metabolism, Dalhousie University, Halifax, NS, Canada;10. Department of Radiology, University British Columbia, Vancouver, BC, Canada;11. Cancer Care Ontario, Toronto, ON, Canada
Abstract:Functional Sliced Inverse Regression (FSIR) and Functional Sliced Average Variance Estimation (FSAVE) are two popular functional effective dimension reduction methods. However, both of them have restrictions: FSIR is vulnerable to symmetric dependencies and FSAVE has low efficiency for monotone dependencies and is sensitive to the number of slices. To avoid aforementioned disadvantages, a hybrid method of FSIR and FSAVE is developed. Theoretical properties for the hybrid method and the consistency result of the proposed hybrid estimator are derived. Simulation studies show that the hybrid method has better performance than those of FSIR and FSAVE. The proposed method is also applied on the Tecator data set.
Keywords:Effective dimension reduction  Functional regression  Inverse regression
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