2018/10/12 by Mohamed Ndaoud, Ndaoud, Mohamed
Computer Science · Engineering · Mathematics · #Control Systems and Identification #Distributed Sensor Networks and Detection Algorithms #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1810.05478
openalex publication_date 2018/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study a new notion of scaled minimaxity for sparse\nestimation in high-dimensional linear regression model. We present more\noptimistic lower bounds than the one given by the classical minimax theory and\nhence improve on existing results. We recover sharp results for the global\nminimaxity as a consequence of our study. Fixing the scale of the\nsignal-to-noise ratio, we prove that the estimation error can be much smaller\nthan the global minimax error. We construct a new optimal estimator for the\nscaled minimax sparse estimation. An optimal adaptive procedure is also\ndescribed.\n