A Comparison between Nonparametric Approach: Smoothing Spline and B-Spline to Analyze The Total of Train Passengers in Sumatra Island

Drajat Indra Purnama


The train is one of the means of land transportation of the most desirable communities other than ground transportation such as bus or car. This is because the rail has an advantage that is free from congestion. Increasing mobility of people, means of transportation that is free from congestion increasingly in demand. In Indonesia, the only railway in Java and Sumatra. Either in Java or Sumatra Island train passenger numbers have increased every year. Based on data from BPS-Statistics, the number of train passengers in Sumatra during the last five years has increased an average of 14.8 percent per year.  Noparametric regression model that can be used to describe the pattern of data on the number of train passengers in Sumatra Island is smoothing spline regression and B-spline regression. The purpose of this study is to find the most nonparametric regression model to describe the pattern of the relationship between the time and number of train passengers on Sumatra Island. Smoothing spline and B-spline models were compared by looking at the regression curve and the value of Mean Square Error (MSE). The results of this study indicate that smoothing spline model is more appropriate to see the pattern of the relationship between the time and number of train passengers in Sumatra Island. This can be seen from the MSE of smoothing spline models 2,742.801 smaller than the MSE of B-spline models 3,847.657.


spline, smoothing spline, B-spline, train in Sumatra island

Full Text:



G. Wahba, Spline Models for Observational Data, SIAM, CBMS-NSF Regional Conference Series in Applied Mathematics, Philadelphia, 1990, Vol. 59.

W. Hardle, Applied Nonparametric Regression, Springer-Verlag, Berlin, 1994.

K. Doksum, Y.J. Koo, On Spline Estimators and Prediction Intervals in Nonparametric Regression, Computational Statistics and Data Analysis 35 (2000) 67 – 82.

M. P. Wand, A Comparison of Regression Spline Smoothing Procedures, Departments of Biostatistics, School of Public Health, Harvard, 2005.

Z. J. Huang, Local Asymptotic for Polynomial Spline Regression, The Annual Statistics 31 (2003) 1600-1635.

T. J. Hastie, R.J. Tibshirani, Generalized Additive Models, Chapman & Hall, London, 1990.

R. Eubank, Spline Smoothing and Nonparametric Regression, Marcel Dekker, New York, 1988.

N. S. Wood, Generalized Additive Models: an Introduction With R, Boca Raton: Chapman & Hall/CRC, 2006.

J. Wang, L, Yang, Polynomial Spline Confidence Bands for Regression Curves, Statistica Sinica 19 (2009) 325-342.

P. Craven, G. Wahba, Smoothing Noisy Data with Spline Functions: Estimating the Correct, Degree of Smoothing by the Method of Generalized Cross-Validation, Numer Math University of Wisconsin. 31 (1979) 377-403.

T. C. M. Lee, Smoothing Parameter Selection for Smoothing Splines: a Simulation Study, Computational Statistic & Data Analysis 42 (2003) 139-148.

BPS-Statistics. https://www.bps.go.id/linkTableDinamis/view/id/815, accessed on May 19, 2019.

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM

Eksakta: Journal of Sciences and Data Analysis

E-ISSN 2720-9326 and P-ISSN 2716-0459
Published by: 
Faculty of Mathematics and Natural Sciences
Universitas Islam Indonesia, Yogyakarta

Creative Commons License

Jurnal EKSAKTA is licensed under a Creative Commons Attribution ShareAlike 4.0