Nonparametric hazard rate estimation by orthogonal wavelet methods |
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| Institution: | 1. Centre for Mathematics and its Applications, Australian National University, Canberra, ACT, Australia;2. School of Mathematics and Statistics, The University of Birmingham, Birmingham, UK;1. Bureau of Labor Statistics, Census of Fatal Occupational Injuries, 2 Massachusetts Avenue NE, Room 3180, Washington, DC 20212 USA;2. National Institute for Occupational Safety and Health, Division of Safety Research, 1095 Willowdale Road, Mail Stop H-1808, Morgantown, WV 26505 USA;1. Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA), Université catholique de Louvain (UCL), Belgium;2. Département de Mathématiques, Université du Québec à Montréal (UQAM), Canada;3. Faculty of Economics and Business, KU Leuven, Belgium;4. Faculty of Economics and Business, University of Amsterdam, The Netherlands;1. Department of Statistics and Actuarial Science, East China Normal University, China;2. Department of Applied Finance and Actuarial Studies, Macquarie University, Australia |
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| Abstract: | We propose linear and nonlinear wavelet-based hazard rate estimators where the linear estimator is equivalent to a generalized kernel estimator. An asymptotic formula for the mean integrated squared error (MISE) of the nonlinear wavelet-based hazard rate estimator is provided. It is shown that the MISE formula for the nonlinear estimator is available for hazard rates which are smooth only in a piecewise sense, a feature not available for the kernel estimators. |
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