Multifractal analysis is a powerful modeling and estimation framework for the characterization of data dynamics via the fluctuations of its pointwise regularity in time or space. Though successfully applied in a large number of applications in very different contexts, the estimation of parameters related to the data multifractality is an intricate issue for discrete realworld data in non-standard situations, e.g., for small sample size or in the presence of data corruptions. Building upon a recently introduced generic statistical model for log-leaders, specific multiresolution quantities designed for multifractal analysis, the present work proposes a novel robust model and estimator for the multifractality parameter that quantifies the degree of multifractality in data. Our model explicitly accounts for certain data corruptions as outliers in the spectral log-leader domain. Moreover, we propose an original expectation-maximization algorithm for estimating the parameters associated with the model. Several Monte Carlo simulations have been conducted to evaluate the performance of the proposed estimator, which confirm its good performance when compared to standard linear regression in the presence of different additive or multiplicative data perturbations.