Nonparametric kernel regression estimation near endpoints |
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| Affiliation: | 1. Department of Mathematics, Hanyang University, Seongdong-Ku, Haengdang-Dong, Seoul, 133-791, South Korea;2. Department of Statistical Science, Southern Methodist University, Dallas TX 75275, USA;1. Department of Hematology/Oncology, Martin-Luther-University Halle-Wittenberg, Halle (Saale), Germany;2. Department of Gastroenterology, Martin-Luther-University Halle-Wittenberg, Halle (Saale), Germany;3. Nursing Research Unit, Martin-Luther-University Halle-Wittenberg, Halle (Saale), Germany;4. Department of Radiation Oncology, Martin-Luther-University Halle-Wittenberg, Halle (Saale), Germany;1. Division of Gastroenterology & Hepatology, University of Michigan, Ann Arbor, Michigan;3. VA Center for Clinical Management Research, Ann Arbor, Michigan;4. Institute of Health Policy and Innovation, University of Michigan, Ann Arbor, Michigan;5. University of Michigan School of Nursing, Ann Arbor, Michigan;7. Department of Urology, University of Michigan, Ann Arbor, Michigan;1. Masdar Institute of Science and Technology, Abu Dhabi, United Arab Emirates;2. Laboratoire de Statistique Théorique et Appliquée, Université Paris 6, France;1. Department of Mathematics, College of Science, King Khalid University, Abha, 61413, Saudi Arabia;2. Université Grenoble Alpes, Laboratoire AGEIS, EA 7407, AGIM–TIMB Team, UFR SHS, BP 47, 38040 Grenoble cedex 09, France;1. Department of Pharmaceutical Analysis and Nuclear Pharmacy, Faculty of Pharmacy, Comenius University in Bratislava, Odbojárov 10, SK-832 32 Bratislava, Slovak Republic;2. Toxicological and Antidoping Center, Faculty of Pharmacy, Comenius University in Bratislava, Odbojárov 10, SK-832 32 Bratislava, Slovak Republic |
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| Abstract: | When kernel regression is used to produce a smooth estimate of a curve over a finite interval, boundary problems detract from the global performance of the estimator. A new kernel is derived to reduce this boundary problem. A generalized jackknife combination of two unsatisfactory kernels produces the desired result. One motivation for adopting a jackknife combination is that they are simple to construct and evaluate. Furthermore, as in other settings, the bias reduction property need not cause an inordinate increase in variability. The convergence rate with the new boundary kernel is the same as for the non-boundary. To illustrate the general approach, a new second-order boundary kernel, which is continuously linked to the Epanechnikov (1969, Theory Probab. Appl. 14, 153–158) kernel, is produced. The asymptotic mean square efficiencies relative to smooth optimal kernels due to Gasser and Müller (1984, Scand. J. Statist. 11, 171–185), Müller (1991, Biometrika 78, 521–530) and Müller and Wang (1994, Biometrics 50, 61–76) indicate that the new kernel is also competitive in this sense. |
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