We propose a wavelet based regression function estimator for the estimation of the regression function for a sequence of ?-missing random variables with a common one-dimensional probability density function. Some asymptotic properties of the proposed estimator based on block thresholding are investigated. It is found that the estimators achieve optimal minimax convergence rates over large classes of functions that involve many irregularities of a wide variety of types, including chirp and Doppler functions and jump discontinuities.