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 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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