The Effect of Reparameterisation on the Behaviour of Nonlinear Estimates
This thesis discussed nonlinear modeling and measures o f nonlinear behaviour. A set of data, representing the average weight of dried to bacco leaves (in Several nonlinear models were used to fit the data, however only the Gompertz and the Logistic models were found to be suitable. The estimates...
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| Format: | Thesis |
| Language: | English English |
| Published: |
2000
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| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/9551/1/FSAS_2000_4.pdf http://psasir.upm.edu.my/id/eprint/9551/ |
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| Summary: | This thesis discussed nonlinear modeling and measures o f nonlinear
behaviour. A set of data, representing the average weight of dried to bacco
leaves (in Several nonlinear models were used to fit the data, however only the
Gompertz and the Logistic models were found to be suitable. The estimates of
the para meters were calculated by using the Gauss-Ne wton algorithm in SPLUS
Programming Language.
A good estimator was the one which had the proper ties closed to the
behaviour of a ilnear estimate . The non ilnear behaviour of the estimates was
assessed using two different approaches, namely the analytical and the
empirical approaches. These approaches were employed so that they could
complement the existence of any laggings. The study showed that the analytical approach of curvature measures of Bates
and Watts could measure the average nonlinearity but could not determine the
parameters that cause d the nonlinear behaviour. Mean while, the bias formula
of Box could only give the percentage of the extent to which the parameter
estimates may exceed or fall short of the true parameter value, but could not
be used to compare different parameterizations.
An advantage of using direct measure of skewness of Hougaard was that it
was scale-in dependent and could be used to measure nonlinearity in different
parameterizations. The empirical approach of simulation studies had
successfully revealed the full extent of the nonlinear behaviour of the
estimates an d at the same time, suggested useful reparameterizations.
Reparameterization was used in order to remove or reduce the nonlinear
behaviour of the parameter estimates. The study showed that the nonlinear
behaviour of the parameter estimates was successfully reduced after
reparameterization. The Logistic model in a reparameterized model function
was found to best fit the data as it has the lo therefore the closest-to-linear behaviour. |
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