Based on the theory for M
-estimation of the location parameters. the influence functions of the Lp
estimation (one dimension and multi-dimension) have been derived and the robustness of Lp
estimation has been analyzed while the observational errors obey the contaminated distribution which the data include the outliers disturbed. and the asymptotic variance and efficiency of Lp
estimation have been determined too. The properties of Lp
estimation have been discussed in the both robustness and efficiency. The observations with outliers disturbed can be processed using Lp
estimation which the parameter p
should be between 1.2 and 1.5.