Date of Award


Degree Name

Doctor of Philosophy




This study estimates the location shift parameter in the two-sample problem. The classical method, Least Square(LS), obtains the shift parameter estimate under the normality assumption. A departure from normality assumption makes the estimate inefficient and unreliable. One alternative to the least square estimate is Hodges-Lehmann (HL) estimate which uses Wilcoxon ranks to estimate the shift parameter. This estimate is robust against contaminations and large outliers. The proposed method in this study combines two samples and uses convolution technique to find a density function for the combined sample. This new density function is later used in the construction of the log likelihood function. By the quasi convexity of log likelihood function, a minimization procedure finds the estimate of the shift parameter. Asymptotic properties of this estimator is established under conditions that are similar to those used in LS and HL. Among those properties, the asymptotic linearity and asymptotic normality conditions are satisfied and found in the latter case. As shown in the study, the proposed estimator is highly efficient and robust against contaminations and outliers. This result is supported by the real data examples and by a bootstrap simulation study.

Access Setting

Dissertation-Open Access