Comparison of Scale Estimators for Testing Against Umbrella Alternative

Year 2017, Volume: 30 Issue: 3, 131 - 138, 20.09.2017

O. Ufuk Ekiz , Hamza Gamgam

Abstract

To test null hypothesis against umbrella alternative
for scale parameters,



















 statistic based on
scale estimator is proposed in [1]. In this study,

 statistics based on
different estimators of scale parameters are compared according to type I error
,

 ,
and power. For

 and given values
of  

,

,

, the results are obtained using the data is generated from
exponential and normal distributions in simulation design. According to the
simulation results, when the data generated from normal distribution, the power
value of test statistics based on robust estimators is almost same to the ones
based on parametric estimator as the sample size increases. Moreover, similar
results are obtained when the data is generated from exponential distribution.

Keywords

Umbrella Alternatives, Trimmed Variance, Winsorized Variance

References

• Singh, P. and Liu, W, (2006), A Test Against an Umbrella Ordered Altenatives,
• Computational Statistics & Data Analysis, 51, 1957-1964