Robust percentile bootstrap test with modified one-step M-estimator (MOM): An alternative modern statistical analysis

Normality and homoscedasticity are two main assumptions that must be fulfilled when dealing with classical parametric tests for comparing groups. Any violation of the assumptions will cause the results to be invalid. However, in reality, these assumptions are hardly achieved. To overcome such proble...

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Main Author:	Nurul Hanis, Harun
Format:	Thesis
Language:	eng eng
Published:	2015
Subjects:	QA299.6-433 Analysis
Online Access:	https://etd.uum.edu.my/5324/1/s812430.pdf https://etd.uum.edu.my/5324/2/s812430_abstract.pdf
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id	my-uum-etd.5324
record_format	uketd_dc
institution	Universiti Utara Malaysia
collection	UUM ETD
language	eng eng
advisor	Md Yusof, Zahayu
topic	QA299.6-433 Analysis
spellingShingle	QA299.6-433 Analysis Nurul Hanis, Harun Robust percentile bootstrap test with modified one-step M-estimator (MOM): An alternative modern statistical analysis
description	Normality and homoscedasticity are two main assumptions that must be fulfilled when dealing with classical parametric tests for comparing groups. Any violation of the assumptions will cause the results to be invalid. However, in reality, these assumptions are hardly achieved. To overcome such problem, this study proposed to modify a method known as Parametric Bootstrap test by substituting the usual mean, with a highly robust location measure, modified one step M-estimator (MOM). MOM is an asymmetric trimmed mean. The substitution will make the Parametric Bootstrap test more robust for comparing groups. For this study, the trimming criteria for MOM employed two highly robust scale estimators namely MADn and Tn. A simulation study was conducted to investigate on the performance of the proposed method based on Type I error rates. To highlight the strength and weakness of the method, five variables: number of groups, balanced and unbalanced sample sizes, types of distributions, variances heterogeneity and nature of pairings of sample sizes and group variances were manipulated to create various conditions which are common to real life situations.The performance of the proposed method was then compared with the most frequently used parametric and non parametric tests for two (independent sample t-test and Mann Whitney respectively) and more than two independent groups (ANOVA and Kruskal Wallis respectively). The finding of this study indicated that, for two groups, the robust Parametric Bootstrap test performed reasonably well under the conditions of heterogeneous variances with normal or skewed distributions. While for more than two groups, the test generate good Type I error control under heterogeneous variances and skewed distributions. In comparison with the parametric and non parametric methods, the proposed test outperforms its counterparts under non-normal distribution and heterogeneous variances. The performance of each procedure was also demonstrated using real data. In general, the performance of Type I error for the proposed test is very convincing even when the assumptions of normality and homoscedasticity are violated.
format	Thesis
qualification_name	masters
qualification_level	Master's degree
author	Nurul Hanis, Harun
author_facet	Nurul Hanis, Harun
author_sort	Nurul Hanis, Harun
title	Robust percentile bootstrap test with modified one-step M-estimator (MOM): An alternative modern statistical analysis
title_short	Robust percentile bootstrap test with modified one-step M-estimator (MOM): An alternative modern statistical analysis
title_full	Robust percentile bootstrap test with modified one-step M-estimator (MOM): An alternative modern statistical analysis
title_fullStr	Robust percentile bootstrap test with modified one-step M-estimator (MOM): An alternative modern statistical analysis
title_full_unstemmed	Robust percentile bootstrap test with modified one-step M-estimator (MOM): An alternative modern statistical analysis
title_sort	robust percentile bootstrap test with modified one-step m-estimator (mom): an alternative modern statistical analysis
granting_institution	Universiti Utara Malaysia
granting_department	Awang Had Salleh Graduate School of Arts & Sciences
publishDate	2015
url	https://etd.uum.edu.my/5324/1/s812430.pdf https://etd.uum.edu.my/5324/2/s812430_abstract.pdf
_version_	1747827908719673344
spelling	my-uum-etd.53242021-04-04T08:23:45Z Robust percentile bootstrap test with modified one-step M-estimator (MOM): An alternative modern statistical analysis 2015 Nurul Hanis, Harun Md Yusof, Zahayu Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Arts & Sciences QA299.6-433 Analysis Normality and homoscedasticity are two main assumptions that must be fulfilled when dealing with classical parametric tests for comparing groups. Any violation of the assumptions will cause the results to be invalid. However, in reality, these assumptions are hardly achieved. To overcome such problem, this study proposed to modify a method known as Parametric Bootstrap test by substituting the usual mean, with a highly robust location measure, modified one step M-estimator (MOM). MOM is an asymmetric trimmed mean. The substitution will make the Parametric Bootstrap test more robust for comparing groups. For this study, the trimming criteria for MOM employed two highly robust scale estimators namely MADn and Tn. A simulation study was conducted to investigate on the performance of the proposed method based on Type I error rates. To highlight the strength and weakness of the method, five variables: number of groups, balanced and unbalanced sample sizes, types of distributions, variances heterogeneity and nature of pairings of sample sizes and group variances were manipulated to create various conditions which are common to real life situations.The performance of the proposed method was then compared with the most frequently used parametric and non parametric tests for two (independent sample t-test and Mann Whitney respectively) and more than two independent groups (ANOVA and Kruskal Wallis respectively). The finding of this study indicated that, for two groups, the robust Parametric Bootstrap test performed reasonably well under the conditions of heterogeneous variances with normal or skewed distributions. While for more than two groups, the test generate good Type I error control under heterogeneous variances and skewed distributions. In comparison with the parametric and non parametric methods, the proposed test outperforms its counterparts under non-normal distribution and heterogeneous variances. The performance of each procedure was also demonstrated using real data. In general, the performance of Type I error for the proposed test is very convincing even when the assumptions of normality and homoscedasticity are violated. 2015 Thesis https://etd.uum.edu.my/5324/ https://etd.uum.edu.my/5324/1/s812430.pdf text eng public https://etd.uum.edu.my/5324/2/s812430_abstract.pdf text eng public http://sierra.uum.edu.my/record=b1261740~S1 masters masters Universiti Utara Malaysia Babu, G. 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