Mathematics and Statistics Vol. 11(2), pp. 385 - 399
DOI: 10.13189/ms.2023.110218
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A Glimpse of Nonparametric Single and Double Residual Bootstrap Method with Outliers

Nor Iza Anuar Razak , Zamira Hasanah Zamzuri ^*
School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Malaysia

ABSTRACT

The significance of a model is affected by outliers. The outliers can affect the effectiveness of structural equation modeling (SEM). Here we describe and investigate the behavior of the nonparametric single and double residual bootstrap (DRB) methods in the presence of outliers when applied to SEM. Our study also intends to shorten the computational time of the standard double bootstrap by using an alternative double bootstrap approach. We demonstrate our proposed method by conducting a Monte Carlo experiment series for clean normal Gaussian distributions and contaminated data. The simulation studies were manipulated with different sample sizes, effect sizes, and 10% of contamination in the Y direction. The performance of the proposed method is evaluated using standard measurements and the construction of confidence intervals. The reasonably close parameter and bootstrap estimates suggest that the nonparametric single and double residual bootstrap is an excellent method. The DRB method showed a robust declining pattern for standard measurement estimates and shorter confidence intervals compared to the single residual bootstrap method in both normal and contaminated data. Also, the double bootstrap method takes twice as long as the single bootstrap method to compute. The DRB method is straightforward but demands slightly more computational time and better prediction approximation. This study offers additional perspectives to fellow researchers considering using the nonparametric single and alternative DRB methods with contaminated data.

KEYWORDS
Double Bootstrap, Outliers, Confidence Interval, Simulation, Structural Equation Modeling

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Nor Iza Anuar Razak , Zamira Hasanah Zamzuri , "A Glimpse of Nonparametric Single and Double Residual Bootstrap Method with Outliers," Mathematics and Statistics, Vol. 11, No. 2, pp. 385 - 399, 2023. DOI: 10.13189/ms.2023.110218.

(b). APA Format:
Nor Iza Anuar Razak , Zamira Hasanah Zamzuri (2023). A Glimpse of Nonparametric Single and Double Residual Bootstrap Method with Outliers. Mathematics and Statistics, 11(2), 385 - 399. DOI: 10.13189/ms.2023.110218.