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Activity Number:
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383
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Type:
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Contributed
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Date/Time:
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Tuesday, August 4, 2009 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Physical and Engineering Sciences
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| Abstract - #304293 |
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Title:
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Explicit and Efficient Estimation for a Flexible Class of Stochastic Differential Equation Models
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Author(s):
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Julie L. Forman*+ and Michael Sørensen
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Companies:
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University of Copenhagen and University of Copenhagen
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Address:
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Oester Farimagsgade 5, Opgang B, Department of Biostatistics, Copenhagen, International, 1014, Denmark
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Keywords:
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diffusion models ; martingale estimating function ; non-linear models ; Pearson system ; stochastic differential equation ; stochastic volatility
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Abstract:
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The statistical analysis of stochastic differential equation models is complicated as the likelihood function rarely is explicitly known. This talk concerns a noteworthy exception; the stochastic differential equation with linear drift and quadratic squared diffusion coefficient. The stationary solutions to these equations have invariant distributions equal to the full Pearson system. We show how parameter estimates for these models can be obtained from explicit quadratic martingale estimating functions that are optimal in the sense of Godambe and Heyde. In addition, it was proved recently that the estimators are efficient in the high frequency setting. The analytical tractability of the Pearson diffusions is inherited by a large class of derived non-linear and non-markovian models.
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