COMPARISON OF SIMPLEX AND NELDER-MEAD OPTIMIZATION METHODS IN QUANTILE REGRESSION FOR BOGOR CITY RAINFALL ANALYSIS

Abstract

Predicting extreme rainfall is crucial for supporting planning in the agricultural sector, infrastructure development, and disaster mitigation in the city of Bogor. However, the asymmetric distribution of daily rainfall and the presence of outliers make linear regression methods less suitable. Quantile regression offers an alternative that captures the influence of explanatory variables across different parts of the data distribution, particularly in the extreme regions. This study compares the Simplex and Nelder-Mead methods for estimating quantile regression parameters on extreme rainfall data in Bogor. Daily rainfall data were obtained from the West Java BMKG Climate Station for the period from May 2024 to April 2025, comprising 365 observations, with four explanatory variables: average temperature, average humidity, sunshine duration, and average wind speed. Modeling was conducted at the 0.75, 0.85, and 0.95 quantiles to represent extreme rainfall. The results show that the Simplex method outperformed Nelder-Mead, as indicated by lower Pinball Loss and Mean Absolute Error (MAE) values at most quantiles. Humidity and average wind speed had a significantly positive effect on extreme rainfall intensity, while average temperature had a negative effect. Sunshine duration showed less consistent effects. Overall, the Simplex method is recommended for quantile regression optimization in extreme rainfall data due to its greater stability and accuracy in generating model parameters. However, this study is limited by the number of explanatory variables and the relatively short observation period. Incorporating additional variables such as air pressure, ENSO index, or topographical data, along with extending the observation period, could improve model accuracy and generalizability in future research.