|
Activity Number:
|
130
|
|
Type:
|
Contributed
|
|
Date/Time:
|
Monday, August 3, 2009 : 8:30 AM to 10:20 AM
|
|
Sponsor:
|
Business and Economic Statistics Section
|
| Abstract - #304928 |
|
Title:
|
Asymptotic Efficiency and Finite-Sample Properties of the Generalized Profiling Estimation of the Parameters in Ordinary Differential Equations
|
|
Author(s):
|
Xin Qi*+ and Hongyu Zhao and Hongyu Zhao
|
|
Companies:
|
Yale University and Yale University and Yale University
|
|
Address:
|
1199 Whitney AVE., Hamden, CT, 06517,
|
|
Keywords:
|
differential equations ; profiled estimation ; consistent ; asymptotic normality
|
|
Abstract:
|
The generalized profiling estimation method developed by Ramsay and colleagues is promising for its computational efficiency and good performance. In this approach, the ODE solution is approximated with a linear combination of basis functions. The coefficients of the basis functions are estimated by a penalized smoothing procedure with an ODE-defined penalty. In this paper we first give an upper bound on the uniform norm of the difference between the true solutions and their approximations. Then we use this bound to prove the consistency and asymptotic normality of this estimation procedure. We show that the asymptotic covariance matrix is the same as that of the maximum likelihood estimation. Therefore this procedure is asymptotically efficient. For a fixed sample and the basis functions, we study the limiting behavior of the approximation when the smoothing parameter tends to infinity.
|
