Estimate a Stationary Process under Left Censoring

Let \X_t\ be a stationary signal process interfered by an white noise \Y_t\. The signal X_t is detected and observed only when X_t>Y_t, otherwise only the white noise Y_t is observed. This model is called the left censored model and the observation is called the left censored observation. In this paper we use the nonparametric MLE of the marginal distributions of X_t and Y_t to construct estimates of the mean, autocovariance and autocorrelation functions of the original signal process \X_t\. The strong consistency of the estimates is derived. When \X_t\ is a causal autoregression process, consistent estimates of the autoregression parameters are provided.