Robust Improvements in Ratio-Type Estimators 

Evrim Oral, PhD

 

In sampling theory, when the correlation between study variable Y and auxiliary variable X is positively high, 
the classical ratio estimator is considered to be the most practicable estimator to estimate a population mean. 
Sisodio and Dwivedi [J. Ind. Soc. Agrictural Stat. 33, 1981, p. 13] and Upadhyaya and Singh [Biom. J. 41, 1999, p. 627] 
suggested to use population information of the auxiliary variable such as the coefficient of variation or the 
kurtosis to increase the efficiency of the ratio estimator. Kadilar and Cingi [App. Math. Comp. 151, 2004, p. 893] 
combined this suggestion with the estimators in Ray and Singh [J. Ind. Stat. Assoc. 19, 1981, p. 147] and suggested 
novel ratio estimators for the population mean of the study variable in simple random sampling. 
In this study, we adapt a robust regression method to the estimators suggested by Kadilar and Cingi (2004) and 
obtain the conditions where these adapted estimators are more efficient than the Kadilar-Cingi estimators theoretically. 
We support the theoretical results with several simulations and compare these adapted estimators both with 
Kadilar-Cingi estimators and the classical ratio estimator.

 

Keywords: Ratio type estimators, simple random sampling, robust regression, modified maximum likelihood methodology.

 

This is joint work with Cem Kadilar