2007/12/18 by Jonas Kahn, Kahn, Jonas
Computer Science · Decision Sciences · Engineering · #62G05 #62P35 #81V80 #Control Systems and Identification #FOS: Mathematics #Scientific Measurement and Uncertainty Evaluation #Statistics Theory (math.ST) #Target Tracking and Data Fusion in Sensor Networks
paper · pdf · doi:10.48550/arxiv.0712.2912
openalex publication_date 2007/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper deals with a non-parametric problem coming from physics, namely quantum tomography. That consists in determining the quantum state of a mode of light through a homodyne measurement. We apply several model selection procedures: penalized projection estimators, where we may use pattern functions or wavelets, and penalized maximum likelihood estimators. In all these cases, we get oracle inequalities. In the former we also have a polynomial rate of convergence for the non-parametric problem. We finish the paper with applications of similar ideas to the calibration of a photocounter, a measurement apparatus counting the number of photons in a beam. Here the mathematical problem reduces similarly to a non-parametric missing data problem. We again get oracle inequalities, and better speed if the photocounter is good.