International Journal of Statistics and Applied Mathematics
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International Journal of Statistics and Applied Mathematics

2022, Vol. 7, Issue 4, Part A

A comparative study of wild bootstrap and robust wild bootstrap estimates in linear regression


Author(s): Bello Abdukadir Rasheed, Robiah Adnan, Salisu Lakunti and Usamatu Usman

Abstract: The Wild Bootstrap techniques are widely used today in many other fields like economics, Engineering, and medicine. Imperial evidences indicate that the use of wild bootstrap techniques may produce efficient estimate in the presence of heteroscedasticity error variance. However, in the presence of outliers the wild bootstrap is no longer efficient. It is now evidence that the robust wild Bootstrap technique based on MM-estimator was introduced to handle the outlier’s problems. However, presence of high leverage outliers will introduce wrong parameter estimate and the robust wild Bootstrap is not resistance to high leverage outliers. Hence this research investigates the use of modified robust wild bootstrap techniques on regression model as an estimator in a situation where heteroscedasticity, outliers and high leverage outliers are presence. This paper proposed a modified robust wild bootstrap GM-estimator of MR Boot Wu and MR Boot Liu algorithm based on the weighted residuals which incorporate the Huber weighted function, GM-estimators, robust location and scale, and the wild bootstrap sampling procedure of Wu and Liu. The GM-estimator, was obtain using the MM-estimator as the initial and scale estimator. However, the MR Boot Wu and MR Boot Liu were obtained through a robust wild bootstrap MM-estimator (R Boot). Finally, the real data obtain from twenty-two countries based on their cross country variation on the level of income per capital in the Organization for European Economic Co-operation and Development (OECD) and simulation study. The performances of the MR Boot Wu and MR Boot Wu together with the existing, Boot Wu, Boot Liu, R Boot Wu and R Boot Liu estimators were compared using the biased, standard error and RMSE. The numerical examples indicated that the MR Boot Wu and MR Boot Liu estimator has proven to be a good alternative estimator for economic use.

Pages: 36-41 | Views: 88 | Downloads: 11

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How to cite this article:
Bello Abdukadir Rasheed, Robiah Adnan, Salisu Lakunti, Usamatu Usman. A comparative study of wild bootstrap and robust wild bootstrap estimates in linear regression. Int J Stat Appl Math 2022;7(4):36-41.
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