We consider the problem of estimating an unknown parameter that is observed indirectly by a sensor network. Each of the sensors exhibits probabilistic nonlinear behavior causing censoring (clipping) of the signals at random. The signals then get transmitted over fading wireless channels to the fusion center. We develop three algorithms for estimating the unknown parameter: first is based on Pearson's Method of Moments, which involves the calculation of the statistical moments of the model that can be derive exactly; second is based on the Maximum-Likelihood Estimator, which results in an intractable likelihood function. To evaluate the likelihood function, we develop a novel approximation via a nonparametric probability density estimator that is based on series expansions of the Gram-Charlier family of basis functions; and third is the Marginalized Least Squares in which we solve the least squares problem by marginalizing out the random unknown nuisance parameters of the model. All three algorithms enjoy a low computational complexity, and only involve solving a one-dimensional optimization problem that is simple to implement in practice. We compare the performance of the proposed algorithms under various system configurations and show various tradeoffs between the algorithms as a function of system parameters (e.g., number of sensors, frame length, signal-to-noise ratio, sensing quality etc.).