The robustness of H statistic with hinge estimators as the location measures

The robustness of H statistic with hinge estimators as the location measures

In testing the equality of location measures, the classical tests such as t-test and analysis of variance (ANOVA) are still among the most commonly chosen procedures. These procedures perform best if the assumptions of normality of data and homogeneity of variances are fulfilled. Any violation of t...

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Main Author: Nur Faraidah, Muhammad Di
Format: Thesis
Language:eng
eng
Published: 2014
Subjects:
QA273-280 Probabilities
Mathematical statistics
Online Access:https://etd.uum.edu.my/4415/1/s806323.pdf
https://etd.uum.edu.my/4415/12/s806323_abstract.pdf
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id my-uum-etd.4415
record_format uketd_dc
institution Universiti Utara Malaysia
collection UUM ETD
language eng
eng
advisor Syed Yahaya, Sharipah Soaad
Abdullah, Suhaida
topic QA273-280 Probabilities
Mathematical statistics
spellingShingle QA273-280 Probabilities
Mathematical statistics
Nur Faraidah, Muhammad Di
The robustness of H statistic with hinge estimators as the location measures
description In testing the equality of location measures, the classical tests such as t-test and analysis of variance (ANOVA) are still among the most commonly chosen procedures. These procedures perform best if the assumptions of normality of data and homogeneity of variances are fulfilled. Any violation of these assumptions could jeopardize the result of such classical tests. However, in real life, these assumptions are often violated, and therefore, robust procedures may be preferable. This study proposed two robust procedures by integrating H statistic with adaptive trimmed mean using hinge estimators, HQ and HQ₁. The proposed procedures are denoted as HTᵸᵟ and HTᵸᵟ₁ respectively. H statistic is known for its ability to control Type I error rates while ̂Tᵸᵟ and ̂Tᵸᵟ₁ are the robust location estimators. The method of adaptive trimmed mean trims data using asymmetric trimming technique, where the tail of the distribution is trimmed based on the characteristic of that particular distribution. To investigate on the performance (robustness) of the procedures, several variables were manipulated to create conditions which are known to highlight its strengths and weaknesses. Such variables are the amount of trimming, number of groups, balanced and unbalanced sample sizes, type of distributions, variances heterogeneity and nature of pairings. Bootstrap method was used to test the hypothesis since the distribution of H statistic is unknown. The integration between H statistic and adaptive trimmed mean produced robust procedures that are capable of addressing the problem of violations of the assumptions. The findings showed that the proposed procedures performed best in terms of controlling the Type I error rate with different trimming amounts; the HTᵸᵟ performed best with 20% trimming, while 15% was best for the ̂HTᵸᵟ₁. In addition, both procedures were also proven to be more robust than the classical tests of parameteric (t-test and ANOVA) and non-parametric (Mann Whitney and Kruskal-Wallis).
format Thesis
qualification_name masters
qualification_level Master's degree
author Nur Faraidah, Muhammad Di
author_facet Nur Faraidah, Muhammad Di
author_sort Nur Faraidah, Muhammad Di
title The robustness of H statistic with hinge estimators as the location measures
title_short The robustness of H statistic with hinge estimators as the location measures
title_full The robustness of H statistic with hinge estimators as the location measures
title_fullStr The robustness of H statistic with hinge estimators as the location measures
title_full_unstemmed The robustness of H statistic with hinge estimators as the location measures
title_sort robustness of h statistic with hinge estimators as the location measures
granting_institution Universiti Utara Malaysia
granting_department Awang Had Salleh Graduate School of Arts & Sciences
publishDate 2014
url https://etd.uum.edu.my/4415/1/s806323.pdf
https://etd.uum.edu.my/4415/12/s806323_abstract.pdf
_version_ 1747827734183149568
spelling my-uum-etd.44152016-04-25T01:02:41Z The robustness of H statistic with hinge estimators as the location measures 2014 Nur Faraidah, Muhammad Di Syed Yahaya, Sharipah Soaad Abdullah, Suhaida Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduated School of Art and Sciences QA273-280 Probabilities. Mathematical statistics In testing the equality of location measures, the classical tests such as t-test and analysis of variance (ANOVA) are still among the most commonly chosen procedures. These procedures perform best if the assumptions of normality of data and homogeneity of variances are fulfilled. Any violation of these assumptions could jeopardize the result of such classical tests. However, in real life, these assumptions are often violated, and therefore, robust procedures may be preferable. This study proposed two robust procedures by integrating H statistic with adaptive trimmed mean using hinge estimators, HQ and HQ₁. The proposed procedures are denoted as HTᵸᵟ and HTᵸᵟ₁ respectively. H statistic is known for its ability to control Type I error rates while ̂Tᵸᵟ and ̂Tᵸᵟ₁ are the robust location estimators. The method of adaptive trimmed mean trims data using asymmetric trimming technique, where the tail of the distribution is trimmed based on the characteristic of that particular distribution. To investigate on the performance (robustness) of the procedures, several variables were manipulated to create conditions which are known to highlight its strengths and weaknesses. Such variables are the amount of trimming, number of groups, balanced and unbalanced sample sizes, type of distributions, variances heterogeneity and nature of pairings. Bootstrap method was used to test the hypothesis since the distribution of H statistic is unknown. The integration between H statistic and adaptive trimmed mean produced robust procedures that are capable of addressing the problem of violations of the assumptions. The findings showed that the proposed procedures performed best in terms of controlling the Type I error rate with different trimming amounts; the HTᵸᵟ performed best with 20% trimming, while 15% was best for the ̂HTᵸᵟ₁. In addition, both procedures were also proven to be more robust than the classical tests of parameteric (t-test and ANOVA) and non-parametric (Mann Whitney and Kruskal-Wallis). 2014 Thesis https://etd.uum.edu.my/4415/ https://etd.uum.edu.my/4415/1/s806323.pdf text eng validuser https://etd.uum.edu.my/4415/12/s806323_abstract.pdf text eng public masters masters Universiti Utara Malaysia Babu, G. J., Padmanabhan, A. R., & Puri, M. L. (1999). Robust one-way ANOVA under possibly non-regular conditions. Biometrical Journal, 321-339. Baguio, C. B. (2008). Trimmed mean as an adaptive robust estimator of a location parameter for Weibull Distribution. World Academy of Science, Engineering and Technology, 681-686. Bradley, J. V. (1978). Robustness? 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