# Pemodelan Nonparametric Regression Modeling Based on Spline Truncated Estimator on Simulation Data

## Authors

• Ghony N Nurhuda Universitas Mulawarman
• Wasono Wasono Universitas Mulawarman
• Darnah Andi Nohe Universitas Mulawarman

## Keywords:

Parametric Regression, Nonparametric Regression, Spline Truncated, Simulation

## Abstract

Regression analysis is one of the statistical analysis used to estimate the pattern of the relationship between predictor variables and response variables . In general, the approach to estimating the regression function is the parametric regression, the nonparametric regression and the semiparametric regression. The approach with parametric regression is used if the shape of the regression curve is assumed to follow a certain pattern such as linear, quadratic, cubic and so on, but in fact there is an unknown pattern of relationship between predictor variables and response variables, so nonparametric regression is used. Then the combination of parametric and nonparametric regression is semiparametric regression. One of the well-known nonparametric regression estimators is the spline truncated. This study was conducted by simulating the relationship pattern of the response variable and the predictor variable that not have specific pattern by following a trigonometric function that formed a regression curve with a standard deviation of 0,05 and 0,25 which formed a different distribution of data, then will be approached with parametric regression (linear, quadratic, cubic) and nonparametric regression (spline truncated linear). Based on the coefficient of determination of each standard deviation, it will shows that the nonparametric regression approach has high flexibility so that it is able to adjust the form of regression curve estimation by itself

## References

Budiantara, I. N., 2001. Regresi Nonparametrik dan Semiparametrik Serta Perkembangannya. In Makalah Pembicara Utama pada Seminar Nasional Alumni Pasca Sarjana Matematika Universitas Gadjah Mada, Yogyakarta.

Budiantara, I. N., 2005. Penentuan titik-titik knots dalam regresi spline. Jurnal Jurusan Statistika FMIPA-ITS.

Dani, A. T. R., Adrianingsih, N. Y., Ainurrochmah, A., & Sriningsih, R., 2021. Flexibility of Nonparametric Regression Spline Truncated on Data without a Specific Pattern. Jurnal Litbang Edusaintech, 2(1), 37-43.

Dani, A. T. R., & Ni'matuzzahroh, L., 2021. Pemodelan Persentase Penduduk Miskin Kabupaten/Kota di Provinsi Jawa Barat dengan Pendekatan Regresi Nonparametrik Spline Truncated. J Statistika: Jurnal Ilmiah Teori Dan Aplikasi Statistika, 14(1), 24-29.

Dani, A. T. R., Ratnasari, V., & Budiantara, I. N., 2021. Optimal Knots Point and Bandwidth Selection in Modeling Mixed Estimator Nonparametric Regression. In IOP Conference Series: Materials Science and Engineering (Vol. 1115, No. 1, p. 012020). IOP Publishing.

Darnah, 2019. Modeling of Maternal Mortality and Infant Mortality Cases in East Kalimantan using Poisson Regression Approach Based on Local Linier Estimator. IOP Conf. Series : Earth and Environmental Science 243

Eubank, R. L., 1999. Nonparametric Regression and Spline Smoothing, Second Edition. Marcel Dekker Inc. New York.

Gujarati, D. N., 2003. Ekonometrika Dasar, Terjemahan: Sumarno Zain. Erlangga. Jakarta.

Gujarati, D. N., 2006. Dasar-dasar Ekonometrika Jilid 1 dan 2. Edisi Ketiga. Erlangga. Jakarta.

Hardle, W., 1990. Applied Nonparametric Regression. Cambridge University Press. New York.

Iqbal, M.,, 2015. Regresi Data Panel (2): Tahap Analisis. Retrived From https://dosen. perbanas. id/regresi-data-panel-2-tahap-analisis.

Lestari, B., Budiantara, I. N., & Chamidah, N., 2019. Smoothing parameter selection method for multiresponse nonparametric regression model using smoothing spline and kernel estimators approaches. In Journal of Physics: Conference Series (Vol. 1397, No. 1, p. 012064). IOP Publishing.

Nohe, D.A., 2014. Biostatistika 1. Halaman Moeka. Jakarta Barat.

Prahutama, A., & Santoso, R. 2018. Mix local polynomial and spline truncated: the development of nonparametric regression model. In Journal of Physics: Conference Series (Vol. 1025, No. 1, p. 012102). IOP Publishing.

Widodo, E., & Irmayanti, A. N., 2019. Perbandingan Metode Regresi Spline Truncated dengan Regresi Linear Sederhana untuk Kasus Harga Saham Perusahaan Pertambangan di Indonesia. EKSAKTA: Journal of Sciences and Data Analysis, 143-153