Development and modification of H-statistic with winsorized approach means

Development and modification of H-statistic with winsorized approach means

Student’s t-test and ANOVA F-test are the classical statistical tests for comparing two or more independent groups. Both are powerful tests when data is normally distributed and variances are homogenous. However, the data with these properties sometime is difficult to be met in real-life will affect...

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Main Author: Teh, Kian Wooi
Format: Thesis
Language:eng
eng
Published: 2017
Subjects:
QA273-280 Probabilities
Mathematical statistics
Online Access:https://etd.uum.edu.my/6991/1/s811121_01.pdf
https://etd.uum.edu.my/6991/2/s811121_02.pdf
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id my-uum-etd.6991
record_format uketd_dc
institution Universiti Utara Malaysia
collection UUM ETD
language eng
eng
advisor Abdullah, Suhaida
Md. Yusof, Zahayu
topic QA273-280 Probabilities
Mathematical statistics
spellingShingle QA273-280 Probabilities
Mathematical statistics
Teh, Kian Wooi
Development and modification of H-statistic with winsorized approach means
description Student’s t-test and ANOVA F-test are the classical statistical tests for comparing two or more independent groups. Both are powerful tests when data is normally distributed and variances are homogenous. However, the data with these properties sometime is difficult to be met in real-life will affect the Type I error rates control and reduce statistical power of the tests. H-statistic is a robust statistic but performs well only under non-normality dataset. This statistic had been invented with MOM estimator denoted as MOM-H. Therefore, in this study, two modified H-statistic with mean using Winsorizing approach are proposed to handle both violated properties. The proposed statistics are the H-statistic with Winsorized mean (WM) and the H-statistic with adaptive Winsorized mean (AWM) which denoted as WM-H and AWM-H, respectively. Using this modification, the tests perform better not only under non-normality, but also under heterogeneity of variances. The approach use predetermined values of 15% and 25% Winsorization. The WM is Winsorizing symmetrically while the AWM is Winsorizing adaptively according to the shape of distribution based on hinge estimators, HQ and HQ₁. The WM-H statistic consists of 15WM-H and 25WM-H, whereas the AWM-H comprises of 15WHQ-H, 25WHQ-H, 15WHQ₁-H and 25WHQ₁-H. The performances of the proposed tests are evaluated using Type I error rates and power of test based on simulation study. All the results from the proposed tests are compared with the original H-statistic, MOM-H and classical statistical tests. The findings indicate that 15WHQ-H performs the best for two groups case especially under heavy tailed distribution. Under skewed distribution, WM-H has better performance to others but comparable to MOM-H. In overall the proposed tests are able to give better results than the MOM-H and the classical statistical tests under certain conditions. The proposed tests are also validated using real dataset.
format Thesis
qualification_name masters
qualification_level Master's degree
author Teh, Kian Wooi
author_facet Teh, Kian Wooi
author_sort Teh, Kian Wooi
title Development and modification of H-statistic with winsorized approach means
title_short Development and modification of H-statistic with winsorized approach means
title_full Development and modification of H-statistic with winsorized approach means
title_fullStr Development and modification of H-statistic with winsorized approach means
title_full_unstemmed Development and modification of H-statistic with winsorized approach means
title_sort development and modification of h-statistic with winsorized approach means
granting_institution Universiti Utara Malaysia
granting_department Awang Had Salleh Graduate School of Arts & Sciences
publishDate 2017
url https://etd.uum.edu.my/6991/1/s811121_01.pdf
https://etd.uum.edu.my/6991/2/s811121_02.pdf
_version_ 1747828141702774784
spelling my-uum-etd.69912021-08-18T08:03:00Z Development and modification of H-statistic with winsorized approach means 2017 Teh, Kian Wooi Abdullah, Suhaida Md. Yusof, Zahayu Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Arts and Sciences QA273-280 Probabilities. Mathematical statistics Student’s t-test and ANOVA F-test are the classical statistical tests for comparing two or more independent groups. Both are powerful tests when data is normally distributed and variances are homogenous. However, the data with these properties sometime is difficult to be met in real-life will affect the Type I error rates control and reduce statistical power of the tests. H-statistic is a robust statistic but performs well only under non-normality dataset. This statistic had been invented with MOM estimator denoted as MOM-H. Therefore, in this study, two modified H-statistic with mean using Winsorizing approach are proposed to handle both violated properties. The proposed statistics are the H-statistic with Winsorized mean (WM) and the H-statistic with adaptive Winsorized mean (AWM) which denoted as WM-H and AWM-H, respectively. Using this modification, the tests perform better not only under non-normality, but also under heterogeneity of variances. The approach use predetermined values of 15% and 25% Winsorization. The WM is Winsorizing symmetrically while the AWM is Winsorizing adaptively according to the shape of distribution based on hinge estimators, HQ and HQ₁. The WM-H statistic consists of 15WM-H and 25WM-H, whereas the AWM-H comprises of 15WHQ-H, 25WHQ-H, 15WHQ₁-H and 25WHQ₁-H. The performances of the proposed tests are evaluated using Type I error rates and power of test based on simulation study. All the results from the proposed tests are compared with the original H-statistic, MOM-H and classical statistical tests. The findings indicate that 15WHQ-H performs the best for two groups case especially under heavy tailed distribution. Under skewed distribution, WM-H has better performance to others but comparable to MOM-H. In overall the proposed tests are able to give better results than the MOM-H and the classical statistical tests under certain conditions. The proposed tests are also validated using real dataset. 2017 Thesis https://etd.uum.edu.my/6991/ https://etd.uum.edu.my/6991/1/s811121_01.pdf text eng public https://etd.uum.edu.my/6991/2/s811121_02.pdf text eng public masters masters Universiti Utara Malaysia Abdullah, S. (2011). Kaedah Alexander-Govern menggunakan penganggar teguh dengan pendekatan pangkasan data: Satu kajian simulasi. (Unpublished Doctoral thesis). Universiti Utara Malaysia, Sintok, Malaysia Ahmad Mahir, R., & Al-Khazaleh, A. M. H. (2009). New method to estimate missing data by using the asymmetrical Winsorized mean in a time series. 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