Sains Malaysiana 48(1)(2019): 237–242

http://dx.doi.org/10.17576/jsm-2019-4801-27

 

On Robust Estimation for Slope in Linear Functional Relationship Model

(Penganggaran Teguh bagi Kecerunan dalam Model Linear Hubungan Fungsian)

 

AZURAINI MOHD ARIF¹, YONG ZULINA ZUBAIRI^2* & ABDUL GHAPOR HUSSIN³

 

¹Institute of Graduate Studies, Universiti Malaya, 50603 Kuala Lumpur, Federal Territory, Malaysia

 

²Centre for Foundation Studies in Science, Universiti Malaya, 50603 Kuala Lumpur, Federal Territory, Malaysia

 

³National Defense University Malaysia, Sungai Besi Camp, 57000 Kuala Lumpur, Federal Territory, Malaysia

 

Received: 29 August 2017/Accepted: 3 August 2018

 

ABSTRACT

In this paper, we propose a robust parameter estimation method for the linear functional relationship model. We improved the maximum likelihood estimation using robust estimators and robust correlation coefficients to estimate the slope parameter. The performance of the propose method, MMLE, is compared with the standard maximum likelihood estimation (MLE) and the nonparametric method in terms of mean square error. The results for simulation studies suggested the performance of the MMLE and nonparametric methods gives better estimate than the standard MLE in the presence of outliers. The novelty of the proposed method is that it is not affected by the presence of outliers and is simple to use. To illustrate practical application of the methods, we obtain the estimate of the slope parameter in a study of body-composition techniques for children.

 

Keywords: Linear functional relationship model; mean square error; modified maximum likelihood estimation; outliers; robust

 

ABSTRAK

Dalam kertas ini, kami mencadangkan kaedah penganggaran parameter teguh bagi model linear hubungan fungsian. Kami menambah baik kaedah kebolehjadian maksimum menggunakan penganggar teguh dan pekali korelasi teguh bagi menganggarkan parameter kecerunan. Kuasa pretasi diukur bagi kaedah yang disyorkan iaitu MMLE, MLE dan kaedah tidak berparameter menggunakan ralat kuasa dua min. Keputusan simulasi menujukkan prestasi bagi kaedah yang disyorkan, MMLE dan kaedah tidak berparameter adalah lebih teguh daripada kaedah kebolehjadian maksimum apabila terdapat data terpencil. Kepentingan kaedah yang dicadangkan adalah ia tidak terjejas dengan kehadiran data terpencil dan juga mudah digunakan. Penggunaan kesemua kaedah yang dicadangkan ditunjukkan melalui data set sebenar dengan kaedah untuk menganggarkan kecerunan model bagi data komposisi badan untuk kanak-kanak.

 

Kata kunci: Kebolehjadian maksimum yang diubah suai; min ralat kuasa dua; model linear hubungan fungsian; teguh; terpencil

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*Corresponding author; email: yzulina@um.edu.my