Tobit maximum-likelihood estimation for stochastic time series affected by receiver saturation

The Tobit (Tobin Probit) model is adapted from the field of econometrics as a maximum likelihood estimator of PDF (probability density function) parameters for data that have been censored and truncated. A general expression for the Tobit estimator is presented. It is shown that when the (standard) maximum likelihood estimator is efficient for the random variable with unlimited dynamic range, the unbiased Tobit estimator is efficient for the censored/truncated random variable. The model is presented in detail for the Rayleigh PDF; its efficiency is confirmed, independent of the degree of truncation/censoring. Results from the application of Tobit estimation to simulated data with Rayleigh, log-normal, Rice-Nakagami, and Nagakami-M PDFs are shown to exhibit very low mean-squared error as well. The limitations and computational complexities of the Tobit estimator are discussed