Abstract: This paper shows that nonparametric estimation of θ for generalized Lehmann's alternative models h(F;θ) is possible, even in the one-sample problem, when symmetry of the basic distribution function F about zero, F(x)=1-F(-x), is assumed. Simultaneous nonparametric estimators of μ and θ for the model h(F(·-μ);θ are also provided under the symmetry of F. The asymptotic normality of these estimators is proved under certain regularity conditions.
Key words and phrases: Lehmann's alternative, nonparametric estimation, one-sample, asymptotic normality.