Reweighting approximate GM estimators: Asymptotics and residual-based graphics |
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| Institution: | 1. Department of Statistics, University of Illinois Urbana-Champaign, Champaign, IL 61820, USA;2. Institute of Statistics, Academia Sinica, Nankang, Taipei, Taiwan;1. Leeds Teaching Hospital Trust, Leeds, United Kingdom;2. Institute of Psychiatry, Psychology and Neuroscience, King''s College London, London, United Kingdom;3. University of Cambridge, Cambridge, United Kingdom;4. South London and Maudsley NHS Foundation Trust, London, United Kingdom;5. Barnet, Enfield and Haringey Mental Health Trust, London, United Kingdom;6. University of Exeter Medical School, Exeter, United Kingdom;7. Stavanger University Hospital, Stavanger, Norway;1. Medical Faculty of the Martin Luther University Halle-Wittenberg and University Hospital Halle (Saale), Department of Visceral, Vascular and Endocrine Surgery, Ernst-Grube-Str. 40, 06120, Halle (Saale), Germany;2. Institute of Medical Biometry and Informatics, University of Heidelberg, Im Neuenheimer Feld 130.3, 69120, Heidelberg, Germany;3. Department of General, Visceral, Vascular, and Thoracic Surgery, Klinikum Frankfurt Höchst, Gotenstraβe 6-8, 65929, Frankfurt am Main, Germany;4. Institute for Quality and Efficiency in Health Care (IQWiG), Im Mediapark 8, 50670, Cologne, Germany;5. University of Queensland, Princess Alexandra Hospital, Brisbane, Australia, Princess Alexandra Hospital, Brisbane, QLD, 4102, Australia;6. Memorial Sloan-Kettering Cancer Center and Weill Cornell Medical College, 1275 York Avenue, New York, NY, 10065, USA;7. The Alliance for Clinical Trials in Oncology (Alliance) Statistics and Data Center, Duke University Medical Center, Hock Plaza, 2424 Erwin Rd, Room 8040, Durham, NC, 27705, USA;8. Department of Digestive and Oncological Surgery, University Hospital C. Huriez, Inserm UMR-S 1172, Jean-Pierre Aubert Research Center (JPARC) Team, 1, Rue Polonovski, 59037, Lille Cedex, France;9. Department of Surgery, Klinikum Rechts der Isar, Technical University Munich, Ismaninger Str. 22, 81675, Munich, Germany;10. Division of Hematology/Oncology, University of Michigan Medical Center, 1500 E Medical Center Drive, C347, SPC 5848 Ann Arbor, MI, 48109, USA;11. Department of Surgery, Leiden University Medical Center, K6-R, P.O. Box 9600, 2300, RC Leiden, the Netherlands;12. Centre Régional de Lutte Contre le Cancer, Val D''Aurelle, Montpellier Cedex 05, France;13. Day Treatment Center (TTZ), Interdisciplinary Tumor Center Mannheim (ITM) & 3rd Department of Medicine, University Medical Centre Mannheim, Medical Faculty Mannheim of the University of Heidelberg, Theodor-Kutzer-Ufer 1-3, 68167, Mannheim, Germany;14. 3rd Department of Internal Medicine (Hematology/Medical Oncology), Klinikum Rechts der Isar, Technische Universität München, Ismaninger Str. 22, 81675, Munich, Germany;1. The Affiliated Luohu Hospital of Shenzhen University Health Sciences Center, Shenzhen, Guangdong, People''s Republic of China;2. Department of Preventive Medicine, Shenzhen University Health Sciences Center, Shenzhen, Guangdong, People''s Republic of China;3. College of Physical Education, Zhengzhou University, Zhengzhou, Henan, People''s Republic of China;4. Department of Epidemiology and Health Statistics, College of Public Health, Zhengzhou University, Zhengzhou, Henan, People''s Republic of China;5. Department of Clinical Medicine, Shenzhen University Health Sciences Center, Shenzhen, Guangdong, People''s Republic of China;1. Department of Cognitive Science, University of California, San Diego, United States;2. Department of Neuroscience, University of California, San Diego, United States;1. Collaboration for Outcomes Research and Evaluation, The University of British Columbia, Vancouver, Canada;2. Department of Internal Medicine, Yale University School of Medicine, New Haven, CT, USA;3. Pharmaceutical Health Services Research, University of Maryland School of Pharmacy, Baltimore, MD, USA;4. Department of Medicine and Community Health Sciences, University of Calgary, Calgary, Canada;5. Division of Respiratory Medicine and Institute for Heart and Lung Health, Vancouver General Hospital, The University of British Columbia, Vancouver, Canada;1. Institute of Cognitive Neuroscience, National Yang-Ming University, Taiwan;2. Department of Applied Chinese Language and Culture, National Taiwan Normal University, Taiwan;3. Institute of Linguistics, National Taiwan University, Taiwan;4. Institute of Linguistics, Academia Sinica, Taiwan;5. Institute of Cognitive Neuroscience, National Central University, Taiwan |
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| Abstract: | The iterative weighted least squares algorithm is handy for solving generalized estimating equations. In some situations it may be desirable to limit the number of iterations to a fixed finite number, for instance, to keep the breakdown point under control. Such a scheme is called reweighting. Usually reweighting leads to a different large sample theory than full iteration, and the reweighted estimator may inherit deficiencies of the starting value. When might the reweighting scheme work? To answer this question we define a broad class of estimators, namely, approximate GM estimators, and we show that reweighting leads to the same large sample theory as full iteration within this class. As an example, we provide conditions under which one-step Newton-Raphson estimators are approximate GM estimators. We then use the reweighting to construct residual-based graphics for approximate GM estimates, adapting weighted residual plots that have been proposed previously, and developing new plots to provide complementary views of the data. |
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