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Abstract Details

Activity Number: 297
Type: Contributed
Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
Sponsor: Biometrics Section
Abstract - #304560
Title: Estimating Parameters of an Ode Model: Data Augmentation to Overcome Small Sample Problem
Author(s): Arun Kumar*+ and Hongqi Xue and Hulin Wu
Companies: Indian Institute of Management, Indore and University of Rochester and University of Rochester
Address: Faculty Block-B, First Floor, Indore 453331, , India
Keywords: Ordinary Differential Equations ; Data Augmentation ; Two stage method
Abstract:

Estimating parameters of an Ordinary Differential Equation (ODE) model with small sample is a problem that is regularly encountered in biomedical studies. We propose data augmentation to overcome the problem. The proposed method for data augmentation is easy to implement with any two stage method for estimating parameters of an ODE model. In a two stage method, first a statistical model is fitted to the data and then the smoothed data are used in the second stage to estimate the parameters. Fitted statistical model, however, can also be used to get more observations through interpolation. Simulation studies show that data augmentation does improve the parameter estimates of an ODE model but with a caveat. The relationship between the error in the estimates and the sample size of the augmented data set is non-linear i.e. beyond a particular sample size adding more data may make the estimates worse.


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