PEMODELAN STATISTICAL DOWNSCALING DENGAN LASSO DAN GROUP LASSO UNTUK PENDUGAAN CURAH HUJAN
Keywords:group lasso, lasso, rainfall, statistical downscaling
One of the rainfall prediction techniques is the Statistical Downscaling Modeling (SDS). SDS modeling is one of the applications of modeling with covariates conditions that are generally large and not independent. The problems that will be encountered is the problem of ill-conditional data i.e multicollinearity and the high correlation between variables. The case of highly correlated data causes a linear regression coefficient estimators obtained to have a large variance. This research was conducted to make the statistical downscaling modeling using the lasso and group lasso for the prediction of rainfall. Group of the covariate scenario is applied based on the adjacent area, the high correlation between covariates and correlation between covariates and responses, and also the addition of dummy variables. Scenario six (grouping which is done by considering the covariates that have a positive correlation to the response is divided into 3 groups, 1 individual and the covariates that are negatively correlated with the response are divided into 2 groups, 1 individual) is better than the other scenarios in linear modeling without a dummy. Then, linear modeling with a dummy is better than without a dummy for both techniques. In linear modeling with a dummy, the Group lasso technique can be considered more in SDs modeling, because the difference in the RMSEP statistical value and the correlation coefficient value is significant.
Bakin, S. (1999). Adaptive regression and model selection in data mining problems [thesis]. Canberra (AU): The Australian National University.
Efron, B., Hastie, T., Johnstone, I., & Tibshirani, R. (2004). Least Angle Regression. The Annals of Statistics, 32(2): 407â€“499.
Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. New York (US): Springer Science & Business Media.
Huang, J., & Zhang, T. (2010). The Benefit of Group Sparsity. The Annals of Statistics, 38(4): 1978â€“2004.
Lounici, K., Pontil, M., Van De Geer, S., Tsybakov, A. B., & others. (2011). Oracle Inequalities and Optimal Inference Under Group Sparsity. The Annals of Statistics, 39(4): 2164â€“2204.
Makridakis, S., Wheelwright, S. C., & McGee, V. E. (1999). Metode dan Aplikasi Peramalan. Jakarta: Erlangga.
Nardi, Y., & Rinaldo, A. (2008). On the Asymptotic Properties of the Group Lasso Estimator for Linear Models. Electronic Journal of Statistics, 2: 605â€“633.
Permatasari, S. M., Djuraidah, A., & Soleh, A. M. (2017). Statistical Downscaling with Gamma Distribution and Elastic Net Regularization. The 2nd International Conference On Applied Statistics (ICAS 2016), 121â€“129. Bandung (ID): Department of Statistics, UNPAD.
Santri, D., Wigena, A. H., & Djuraidah, A. (2016). Statistical Downscaling Modeling with Quantile Regression Using Lasso to Estimate Extreme Rainfall. AIP Conference Proceedings, 1707(1), 080005. AIP Publishing LLC.
Soleh, A. M., Wigena, A. H., Djuraidah, A., & Saefuddin, A. (2015a). Pemodelan Statistical Downscaling untuk Menduga Curah Hujan Bulanan Menggunakan Model Linier Terampat Sebaran Gamma. Jurnal Informatika Pertanian, 24(2): 215â€“222.
Soleh, A. M., Wigena, A. H., Djuraidah, A., & Saefuddin, A. (2015b). Statistical downscaling to predict monthly rainfall using linear regression with L1 regularization (LASSO). Applied Mathematical Sciences, 9(108): 5361â€“5369.
Tibshirani, R. (1996). Regression Shrinkage and Selection Via the Lasso. Journal of the Royal Statistical Society: Series B (Methodological), 58(1): 267â€“288.
Wang, H., & Leng, C. (2008). A Note on Adaptive Group Lasso. Computational Statistics & Data Analysis, 52(12): 5277â€“5286.
Wigena, A. (2006). Pemodelan statistical downscaling dengan regresi projection pursuit untuk peramalan curah hujan bulanan: kasus curah hujan bulanan di indramayu [disertasi]. Bogor (ID): Institut Pertanian Bogor.
Yuan, M., & Lin, Y. (2006). Model Selection and Estimation in Regression with Grouped Variables. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 68(1): 49â€“67.
Yunus, M., Saefuddin, A., & Soleh, A. M. (2017). Characteristics of Group Lasso in Handling High Correlated Data. Applied Mathematical Sciences, 11(20): 953â€“961.