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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:English
English
Published: 2015
Subjects:
QA299.6-433 Analysis
Online Access:http://etd.uum.edu.my/5324/
http://sierra.uum.edu.my/record=b1261740~S1
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spelling my.uum.etd.53242021-04-04T08:23:45Z http://etd.uum.edu.my/5324/ Robust percentile bootstrap test with modified one-step M-estimator (MOM): An alternative modern statistical analysis Nurul Hanis, Harun 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 NonPeerReviewed text en /5324/1/s812430.pdf text en /5324/2/s812430_abstract.pdf Nurul Hanis, Harun (2015) Robust percentile bootstrap test with modified one-step M-estimator (MOM): An alternative modern statistical analysis. Masters thesis, Universiti Utara Malaysia. http://sierra.uum.edu.my/record=b1261740~S1
institution Universiti Utara Malaysia
building UUM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Utara Malaysia
content_source UUM Electronic Theses
url_provider http://etd.uum.edu.my/
language English
English
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
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
publishDate 2015
url http://etd.uum.edu.my/5324/
http://sierra.uum.edu.my/record=b1261740~S1
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score 13.211869

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