Hinge estimators of location: Robust to asymmetry

Reed, James F.; Stark, David B.

doi:10.1016/0169-2607(95)01708-9

Cited by 35 publications

(41 citation statements)

References 5 publications

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“…The percentage of lower and upper trimming identified using hinge estimator HQ 1 (Reed & Stark, 1996). However the total percentage of trimming is predetermined just like the usual trimmed mean.…”

Section: Upper Trimming Percentage and N Jmentioning

confidence: 99%

“…This adaptive trimmed mean uses hinge estimator HQ 1 (Reed & Stark, 1996) in order to adjust the trimming process that suits the shape of data distribution. Keselman et al (2007) successively improved Welch test using this adaptive trimmed mean in controlling Type I error rates.…”

Section: Adaptive Trimmed Meanmentioning

confidence: 99%

“…Another approach of trimming which was investigated by Keselman, Wilcox, Lix, Algina and Fradette (2007) used fixed asymmetric trimming. This trimming approach uses hinge estimators proposed by Reed and Stark (1996) to determine the suitable amount of trimming on each tail of a distribution. However, their method still adopts the fixed trimming percentages.…”

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confidence: 99%

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Type I Error Rates of Ft Statistic with Different Trimming Strategies for Two Groups Case

Yusof¹,

Abdullah²,

Yahaya³

et al. 2011

MAS

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When the assumptions of normality and homoscedasticity are met, researchers should have no doubt in using classical test such as t-test and ANOVA to test for the equality of central tendency measures for two and more than two groups respectively. However, in real life we do not often encounter with this ideal situation. A robust method known as F t statistic has been identified as an alternative to the above methods in handling the problem of nonnormality. Motivated by the good performance of the method, in this study we proposed to use F t statistic with three different trimming strategies, namely, i) fixed symmetric trimming (10%, 15% and 20%), ii) fixed asymmetric trimming (10%, 15% and 20%) and iii) empirically determined trimming, to simultaneously handle the problem of nonnormality and heteroscedasticity. To test for the robustness of the procedures towards the violation of the assumptions, several variables were manipulated. The variables are types of distributions and heterogeneity of variances. Type I error for each procedures were then be calculated. This study will be based on simulated data with each procedure been simulated 5000 times. Based on the Type I error rates, we were able to identify which procedures (F t with different trimming strategies) are robust and have good control of Type I error. The best procedure that should be taken into consideration is the F t with MOM -T n for normal distribution, 15% fixed trimming for skewed normal-tailed distribution and MOM -MAD n for skewed leptokurtic distribution. This is because, all of the procedures produced the nearest Type I error rates to the nominal level.

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Section: Upper Trimming Percentage and N Jmentioning

confidence: 99%

Section: Adaptive Trimmed Meanmentioning

confidence: 99%

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Type I Error Rates of Ft Statistic with Different Trimming Strategies for Two Groups Case

Yusof¹,

Abdullah²,

Yahaya³

et al. 2011

MAS

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show abstract

“…And, Reed and Stark (1996) proposed two quick-and-dirty skewness measures SK 2 , SK 2 = ( X (1) − XMD) / (XMD − X (n) ), and SK 5 , SK 5 = (X (1) − XM ) / (XM − X (n) ). The form of SK 2 and SK 5 are identical to Q 2 and H 1 .…”

Section: Introductionmentioning

confidence: 99%

“…Note: XMD is the median, XM is the arithmetic mean, T 25 is the [0.25n] trimmed mean (T α ), X (1) and X (n) are the first and last order statistics. Reed and Stark (1996) proposed a set of asymmetric linear estimators or hinge estimators, defined using the following scheme. Set a total trimming proportion to be trimmed from the sample, α.…”

Section: Introductionmentioning

confidence: 99%

Sensitivity Curves for Asymmetric Trimming Hinge Estimators

Stark

Reed

2007

J. Mod. App. Stat. Meth.

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Robust estimators have been developed and tested for symmetric distributions via simulation studies. The primary objective was to show that they are more efficient than the sample mean when used in conjunction with asymmetric distributions. Little attention has been given to how they perform on data that are from asymmetric distributions, or from distributions that have inherent anomalies (messy data). Thus, the behavior of hinge estimators using sensitivity curve are examined.

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A study on skewness and kurtosis estimators of wind speed distribution under indeterminacy

Aslam

2021

Theor Appl Climatol

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Hinge estimators of location: Robust to asymmetry

Cited by 35 publications

References 5 publications

Type I Error Rates of Ft Statistic with Different Trimming Strategies for Two Groups Case

Type I Error Rates of Ft Statistic with Different Trimming Strategies for Two Groups Case

Sensitivity Curves for Asymmetric Trimming Hinge Estimators

A study on skewness and kurtosis estimators of wind speed distribution under indeterminacy

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