The asymptotics for studentized K-Step M-Estimators of location

Abstract

k-step versions M_n ^(k) of studentized M-estimator M_n of location generated by various types of score functions are studied. The rate of approximation of M_n by M_n ^(k) (n → ∞, k fixed) is derived with the aid of the uniform asymptotic linearity results of three-parameters empirical M-processes. While the rate is considerably improved with increasing k for absolutely continuous score functions, it is improved very slowly for functions with jump-discontinuities where it can never be better than O_p(n^-1).

Keywords:

• Asymptotic linearity
• general asymptotics
• general asymptotics
• studentization

Research of the first author was supported by Charles University Grant GAUK-365

Research of the first author was supported by Charles University Grant GAUK-365

Notes

Research of the first author was supported by Charles University Grant GAUK-365