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We propose wavelet- L1 -estimation for non parametric location-scale models from multiple subjects. The advantage of the wavelet is to avoid the restrictive smoothness requirement for the location and scale functions of the traditional smoothing approaches, such as kernel and local polynomial methods. Under a general dependence framework, which allows for longitudinal data and some spatially correlated data, uniform consistency, uniform Bahadur representation, and asymptotic normality for the proposed estimators of the location and scale functions are established. These results can be used to make asymptotically valid statistical inference.

Wavelet- L 1 -estimation for non parametric location-scale models under a general dependence framework