Generalized splines smoothing in generalized additive models via simulation studies
In general, real life’s effects are not linear. To identify and interpret better the phenomena of real life, a flexible statistical approach is needed. Hence, in order to interpret the real phenomena, among many approaches, generalized additive model, GAM, seems to be a good tool to describe t...
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| Main Author: | |
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| Format: | Thesis |
| Language: | English |
| Published: |
2015
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| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/67681/1/FS%202015%2074%20IR.pdf |
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| Summary: | In general, real life’s effects are not linear. To identify and interpret better the phenomena
of real life, a flexible statistical approach is needed. Hence, in order to
interpret the real phenomena, among many approaches, generalized additive model,
GAM, seems to be a good tool to describe the non-linear effects. GAMs are similar
to generalized linear models, GLM, in which the linear combination of explanatory
variable is replaced by linear combination of scatter plot smoothers.
This research aims to study a restriction of GAM which concentrates to investigate
the parameter of location. Therefore, the method in this research is based on GAM
approach. Univariate generalized additive model is applied over special data which
are generated from extreme value families. The simulated data are in stationary
and non-stationary cases. Therefore, in stationary case, the study has focused over
measuring the accuracy of estimation of parameter of location, m. Also, in nonstationary
cases the research has focused on measuring the accuracy of estimation
of parameter of location, mt . Recall that the stationary case has no trend, while the
structure of non-stationary cases are based on trends. The simulated data are belong
to generalized extreme value distribution, GEV, distribution of Gumbel and special
case of generalized pareto distribution, GPD. The GEV and Gumbel distributions
are simulated in four types: stationary case and non-stationary cases which have the
property of non-stationary in location, non-stationary in scale and non-stationary in
location and scale simultaneously. The special case of GPD distribution is simulated
in two types: stationary and non-stationary cases. Thus, there are ten types of special
data which are investigated during this research.
Finally, to evaluate and measure of accuracy of estimation of parameter of location,
a measure of spread is needed. Root mean square of errors as a measure of spread is
applied for these measurements and evaluations. The result of this research strongly
illustrate that the measure of accuracy of estimation of parameter of location which
is obtained based on estimation of univariate GAM, is better than the alternative
calculation which obtains based on maximum likelihood estimation. |
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