Abstract: We consider the problem of inference on an M-estimator of the location of a continuous but unknown density function from a single sample. Four approximate pivots are studied including one derived from the empirical likelihood of Owen (1988). It is argued that first order M-estimator inference is often correct, close to second order, and that two of the four pivots are distinctly better than the others in this regard.
Key words and phrases: Bootstrap likelihood, empirical likelihood, second order accuracy, edgeworth approximation, robustness.