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A Robust Two Sample Procedure to Estimate a Shift Parameter

SYNOPTIC ABSTRACT This study estimates the shift parameter in the two-sample location problem. The proposed method combines the sample X and sample Y which is shifted with an arbitrary shift variable and a convolution technique is used to smooth out the empirical density function of the combined samples. The smoothed empirical density function is later used in the construction of a log likelihood function for the combined sample. The likelihood function is minimized with respect to an arbitrary shift variable to find an estimate of the true shift parameter. As shown in the study, the proposed estimator is asymptotically efficient and robust against contaminations and outliers. This result is supported by an example and by a simulation study.