2025/01/09 by Jaimin Shah, Martina Cardone, Shah, Jaimin +5 · 1 citation
Mathematics · #Audio and Speech Processing (eess.AS) #FOS: Electrical engineering #FOS: Mathematics #Signal Processing (eess.SP) #Statistical Methods and Inference #Statistics Theory (math.ST) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2501.04937
openalex publication_date 2025/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work establishes regularity conditions for consistency and asymptotic normality of the multiple parameter maximum likelihood estimator(MLE) from censored data, where the censoring mechanism is in the form of 1-bit measurements. The underlying distribution of the uncensored data is assumed to belong to the exponential family, with natural parameters expressed as a linear combination of the predictors, known as generalized linear model (GLM). As part of the analysis, the Fisher information matrix is also derived for both censored and uncensored data, which helps to quantify the impact of censoring and assess the performance of the MLE. The choice of GLM allows one to consider a variety of practical examples where 1-bit estimation is of interest. In particular, it is shown how the derived results can be used to analyze two practically relevant scenarios: the Gaussian model with both unknown mean and variance, and the Poisson model with an unknown mean.