Univariate Generalized Additive Models for Simulated Stationary and Non-Stationary Generalized Pareto Distribution

Mostafa Behzadi,Anwar Fitrianto,Mohd Bakri Adam

doi:10.3844/jmssp.2017.169.176

Mostafa Behzadi, Anwar Fitrianto + Show 1 more

Open Access

https://doi.org/10.3844/jmssp.2017.169.176

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Abstract

Generalized additive models as a predictor in regression approaches, are made up over cubic spline basis and penalized regression splines. Despite of linear predictor in GLM, generalized additive models use a sum of smooth functions of covariates as a predictor. The data which are used in this study have generalized Pareto distribution and have been simulated by inversion method. The data are generated in two types, the stationary case and the non-stationary case. The method of root mean square of errors as a method of measurement is used for comparison between power of predictions which are based on penalized regression splines as a method in univariate generalized additive models and linear regression based on maximum likelihood estimation. The finding of this research illustrates that the amount of accuracy of estimation of parameter of location in UGAM approach as an alternative promising of modelling through each specialized GPD's models, has less RMSE in compare with MLE.

Highlights

During early of 1990, generalized Additive models, GAMs, by attempts of Hastie and Tibshirani have been developed (Hastie and Tibshirani, 1990)
Recall that GAMs is based on smooth functions and has ability to predict
The RMSE which is calculated by GAM's estimation is less than MLE's method

Summary

Introduction

During early of 1990, generalized Additive models, GAMs, by attempts of Hastie and Tibshirani have been developed (Hastie and Tibshirani, 1990). Smoothing splines, are basis for model selection (Gu and Wahba, 1991a) with GAMs (Gu and Wahba, 1991b). The splines bases fulfill well in this circumstances, greatly, because spline basis can be illustrated to have good approximation theoretic properties First of all, it should be written a function which has ability to take a sequence of an array of x values to make a model matrix for the spline. Each sub-figure represents a number of specified knots which could describe the function of GAM only for parameter of location. It must be considered to an important matter which emphasizes that the selecting of number of knots should be large enough, which basis functions could provide enough flexibility to illustrate f(x). The non-stationary of GPD distribution function has a trend in its parameter of location, μt (Hamilton, 1994). Based on global and other local landmarks, the final fitted model is impressed proportionally to these landmarks Fig. 1h

Results and Discussions

Conclusion

Funding Information