Mathematics and Statistics Vol. 7(4A), pp. 58 - 64
DOI: 10.13189/ms.2019.070708
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Tree-based Threshold Model for Non-stationary Extremes with Application to the Air Pollution Index Data

Afif Shihabuddin ¹, Norhaslinda Ali ^1,2,*, Mohd Bakri Adam ^1,2
1 Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia
² Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia

ABSTRACT

Air pollution index (API) is a common tool used to describe the air quality in the environment. High level of API indicates the greater level of air pollution which will gives bad impact on human health. Statistical model for high level of API is important for the purpose of forecasting the level of API so that the public can be warned. In this study, extremes of API are modelled using Generalized Pareto Distribution (GPD). Since the values of API are determined by the value of five pollutants namely sulphur dioxide, nitrogen dioxide, carbon monoxide, ozone and suspended particulate matter, data on API exhibit non-stationarity. Standard method for modelling the non-stationary extremes using GPD is by fixing the high constant threshold and incorporating the covariate model in the GPD parameters for data above the threshold to account for the non-stationarity. However, high constant threshold value might be high enough on certain covariate for GPD approximation to be a valid model for extreme values, but not on the other covariates which leads to the violation of the asymptotic basis of GPD model. New method for the threshold selection in non-stationary extremes modelling using regression tree is proposed to the API data. Regression tree is used to partition the API data into a stationary group with similar covariate condition. Then, a high threshold value can be applied within a group. Study shows that model for extremes of API using tree-based threshold gives a good fit and provides an alternative to the model based on standard method.

KEYWORDS
Air Pollution Index, Threshold Exceedances, Generalized Pareto Distribution, Non-stationary, Regression Tree, Tree-based Threshold

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Afif Shihabuddin , Norhaslinda Ali , Mohd Bakri Adam , "Tree-based Threshold Model for Non-stationary Extremes with Application to the Air Pollution Index Data," Mathematics and Statistics, Vol. 7, No. 4A, pp. 58 - 64, 2019. DOI: 10.13189/ms.2019.070708.

(b). APA Format:
Afif Shihabuddin , Norhaslinda Ali , Mohd Bakri Adam (2019). Tree-based Threshold Model for Non-stationary Extremes with Application to the Air Pollution Index Data. Mathematics and Statistics, 7(4A), 58 - 64. DOI: 10.13189/ms.2019.070708.