2018/04/01 by Anatoli Juditsky, Arkadi Nemirovski, Juditsky, Anatoli +1
Engineering · Medicine · #62G05 #FOS: Mathematics #Integrated Circuits and Semiconductor Failure Analysis #Medical Imaging Techniques and Applications #Sparse and Compressive Sensing Techniques #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1804.00355
openalex publication_date 2018/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we build provably near-optimal, in the minimax sense, estimates\nof linear forms and, more generally, "N-convex functionals" (the simplest\nexample being the maximum of several fractional-linear functions) of unknown\n"signal" known to belong to the union of finitely many convex compact sets from\nindirect noisy observations of the signal. Our main assumption is that the\nobservation scheme in question is good in the sense of A. Goldenshluger, A.\nJuditsky, A. Nemirovski, Electr. J. Stat. 9(2) (2015), arXiv:1311.6765, the\nsimplest example being the Gaussian scheme where the observation is the sum of\nlinear image of the signal and the standard Gaussian noise. The proposed\nestimates, same as upper bounds on their worst-case risks, stem from solutions\nto explicit convex optimization problems, making the estimates\n"computation-friendly."\n