Bayesian curve estimation by polynomial of random order |
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| Affiliation: | 1. Department of Economics and Related Studies, University of York, Heslington, York YO10 5DD, United Kingdom;2. Department of Economics, University College London and CReAM, 30 Gordon Street, London WC1H 0AX, United Kingdom;3. Department of Economics, University of Mannheim, L7, 3-5, 68131 Mannheim, Germany;4. Department of Economics, University College London, CReAM and IAB, 30 Gordon Street, London WC1H 0AX, United Kingdom;2. Department of Military Installations, Army Logistical Academy of PLA, No.20 North 1st Road of University Town, Shapingba District, Chongqing 401331, China;3. Sinohydro Corporation Engineering Bureau 15 Co., Ltd., Xi''an, Shaanxi 710065, China |
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| Abstract: | A Bayesian method of estimating an unknown regression curve by a polynomial of random order is proposed. A joint distribution is assigned over both the set of possible orders of the polynomial and the polynomial coefficients. Reversible jumps Markov chain Monte Carlo (MCMC) (Green, Biometrika 82 (1995) 711-32), are used to compute required posteriors. The methodology is extended to polynomials of random order with discontinuities and to piecewise polynomials of random order to handle wiggly curves. The effectiveness of the methodology is illustrated with a number of examples. |
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