Mixture model of spline truncated and kernel in multivariable nonparametric regression

Rismal; I. Nyoman Budiantara; Dedy Dwi Prastyo

doi:10.1063/1.4952565

Mixture model of spline truncated and kernel in multivariable nonparametric regression

Rismal^*, I. Nyoman Budiantara, Dedy Dwi Prastyo

^*Corresponding author for this work

Institut Teknologi Sepuluh Nopember

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

9 Citations (Scopus)

Abstract

Given the data (x_1i, x_2i,., x_pi,t_1i,t_2i,.,t_qi, y_i) with predictors (x_si, t_ki) and response variables y_i are assumed to follow unknown function such that their dependence can be approximated by a nonparametric regression model y=μ(x,t)+ϵ=Σi=1pfs(x)+Σk=1qgk(t)+ϵ. The component fs(x) is approximated by additive spline regression with p-(number of predictors whereas g(t) is approximated by kernel regression with q-number of predictors. The error ϵ is assumed normally distributed with mean zero and constant variance. The objective of this article is to provide the estimators of fs(x) and gk(t) as well as the mixture model μ(x,t) by means of Maximum Likelihood Estimation (MLE) method.

Original language	English
Title of host publication	Innovations Through Mathematical and Statistical Research
Subtitle of host publication	Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics, ICMSS 2016
Editors	Siti Nur Iqmal Ibrahim, Lai Soon Lee, Md. Sohel Rana, Fong Peng Lim, Mai Zurwatul Ahlam Mohd Jaffar, Mohd Shafie Mustafa, Chuei Yee Chen
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735413962
DOIs	https://doi.org/10.1063/1.4952565
Publication status	Published - 2 Jun 2016
Event	2nd International Conference on Mathematical Sciences and Statistics: Innovations Through Mathematical and Statistical Research, ICMSS 2016 - Kuala Lumpur, Malaysia Duration: 26 Jan 2016 → 28 Jan 2016

Publication series

Name	AIP Conference Proceedings
Volume	1739
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	2nd International Conference on Mathematical Sciences and Statistics: Innovations Through Mathematical and Statistical Research, ICMSS 2016
Country/Territory	Malaysia
City	Kuala Lumpur
Period	26/01/16 → 28/01/16

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10.1063/1.4952565

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Rismal, Budiantara, I. N., & Prastyo, D. D. (2016). Mixture model of spline truncated and kernel in multivariable nonparametric regression. In S. N. I. Ibrahim, L. S. Lee, M. S. Rana, F. P. Lim, M. Z. A. Mohd Jaffar, M. S. Mustafa, & C. Y. Chen (Eds.), Innovations Through Mathematical and Statistical Research: Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics, ICMSS 2016 Article 020085 (AIP Conference Proceedings; Vol. 1739). American Institute of Physics Inc.. https://doi.org/10.1063/1.4952565

Rismal, ; Budiantara, I. Nyoman ; Prastyo, Dedy Dwi. / Mixture model of spline truncated and kernel in multivariable nonparametric regression. Innovations Through Mathematical and Statistical Research: Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics, ICMSS 2016. editor / Siti Nur Iqmal Ibrahim ; Lai Soon Lee ; Md. Sohel Rana ; Fong Peng Lim ; Mai Zurwatul Ahlam Mohd Jaffar ; Mohd Shafie Mustafa ; Chuei Yee Chen. American Institute of Physics Inc., 2016. (AIP Conference Proceedings).

@inproceedings{75ee962d95dc4ca4bc8291ba76f52919,

title = "Mixture model of spline truncated and kernel in multivariable nonparametric regression",

abstract = "Given the data (x1i, x2i,., xpi,t1i,t2i,.,tqi, yi) with predictors (xsi, tki) and response variables yi are assumed to follow unknown function such that their dependence can be approximated by a nonparametric regression model y=μ(x,t)+ϵ=Σi=1pfs(x)+Σk=1qgk(t)+ϵ. The component fs(x) is approximated by additive spline regression with p-(number of predictors whereas g(t) is approximated by kernel regression with q-number of predictors. The error ϵ is assumed normally distributed with mean zero and constant variance. The objective of this article is to provide the estimators of fs(x) and gk(t) as well as the mixture model μ(x,t) by means of Maximum Likelihood Estimation (MLE) method.",

author = "Rismal and Budiantara, {I. Nyoman} and Prastyo, {Dedy Dwi}",

note = "Publisher Copyright: {\textcopyright} 2016 Author(s).; 2nd International Conference on Mathematical Sciences and Statistics: Innovations Through Mathematical and Statistical Research, ICMSS 2016 ; Conference date: 26-01-2016 Through 28-01-2016",

year = "2016",

month = jun,

day = "2",

doi = "10.1063/1.4952565",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

editor = "Ibrahim, {Siti Nur Iqmal} and Lee, {Lai Soon} and Rana, {Md. Sohel} and Lim, {Fong Peng} and {Mohd Jaffar}, {Mai Zurwatul Ahlam} and Mustafa, {Mohd Shafie} and Chen, {Chuei Yee}",

booktitle = "Innovations Through Mathematical and Statistical Research",

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Rismal, , Budiantara, IN & Prastyo, DD 2016, Mixture model of spline truncated and kernel in multivariable nonparametric regression. in SNI Ibrahim, LS Lee, MS Rana, FP Lim, MZA Mohd Jaffar, MS Mustafa & CY Chen (eds), Innovations Through Mathematical and Statistical Research: Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics, ICMSS 2016., 020085, AIP Conference Proceedings, vol. 1739, American Institute of Physics Inc., 2nd International Conference on Mathematical Sciences and Statistics: Innovations Through Mathematical and Statistical Research, ICMSS 2016, Kuala Lumpur, Malaysia, 26/01/16. https://doi.org/10.1063/1.4952565

Mixture model of spline truncated and kernel in multivariable nonparametric regression. / Rismal, ; Budiantara, I. Nyoman ; Prastyo, Dedy Dwi.
Innovations Through Mathematical and Statistical Research: Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics, ICMSS 2016. ed. / Siti Nur Iqmal Ibrahim; Lai Soon Lee; Md. Sohel Rana; Fong Peng Lim; Mai Zurwatul Ahlam Mohd Jaffar; Mohd Shafie Mustafa; Chuei Yee Chen. American Institute of Physics Inc., 2016. 020085 (AIP Conference Proceedings; Vol. 1739).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Mixture model of spline truncated and kernel in multivariable nonparametric regression

AU - Rismal,

AU - Budiantara, I. Nyoman

AU - Prastyo, Dedy Dwi

PY - 2016/6/2

Y1 - 2016/6/2

N2 - Given the data (x1i, x2i,., xpi,t1i,t2i,.,tqi, yi) with predictors (xsi, tki) and response variables yi are assumed to follow unknown function such that their dependence can be approximated by a nonparametric regression model y=μ(x,t)+ϵ=Σi=1pfs(x)+Σk=1qgk(t)+ϵ. The component fs(x) is approximated by additive spline regression with p-(number of predictors whereas g(t) is approximated by kernel regression with q-number of predictors. The error ϵ is assumed normally distributed with mean zero and constant variance. The objective of this article is to provide the estimators of fs(x) and gk(t) as well as the mixture model μ(x,t) by means of Maximum Likelihood Estimation (MLE) method.

AB - Given the data (x1i, x2i,., xpi,t1i,t2i,.,tqi, yi) with predictors (xsi, tki) and response variables yi are assumed to follow unknown function such that their dependence can be approximated by a nonparametric regression model y=μ(x,t)+ϵ=Σi=1pfs(x)+Σk=1qgk(t)+ϵ. The component fs(x) is approximated by additive spline regression with p-(number of predictors whereas g(t) is approximated by kernel regression with q-number of predictors. The error ϵ is assumed normally distributed with mean zero and constant variance. The objective of this article is to provide the estimators of fs(x) and gk(t) as well as the mixture model μ(x,t) by means of Maximum Likelihood Estimation (MLE) method.

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DO - 10.1063/1.4952565

M3 - Conference contribution

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T3 - AIP Conference Proceedings

BT - Innovations Through Mathematical and Statistical Research

A2 - Ibrahim, Siti Nur Iqmal

A2 - Lee, Lai Soon

A2 - Rana, Md. Sohel

A2 - Lim, Fong Peng

A2 - Mohd Jaffar, Mai Zurwatul Ahlam

A2 - Mustafa, Mohd Shafie

A2 - Chen, Chuei Yee

PB - American Institute of Physics Inc.

T2 - 2nd International Conference on Mathematical Sciences and Statistics: Innovations Through Mathematical and Statistical Research, ICMSS 2016

Y2 - 26 January 2016 through 28 January 2016

ER -

Rismal , Budiantara IN , Prastyo DD. Mixture model of spline truncated and kernel in multivariable nonparametric regression. In Ibrahim SNI, Lee LS, Rana MS, Lim FP, Mohd Jaffar MZA, Mustafa MS, Chen CY, editors, Innovations Through Mathematical and Statistical Research: Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics, ICMSS 2016. American Institute of Physics Inc. 2016. 020085. (AIP Conference Proceedings). doi: 10.1063/1.4952565

Mixture model of spline truncated and kernel in multivariable nonparametric regression

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