This book investigates the challenges and methodologies for estimating parameters in high-dimensional statistical models, particularly when dealing with inverse problems. It addresses the fundamental difficulties arising from the curse of dimensionality and the ill-posed nature of inverse problems, where small errors in measurements can lead to large errors in the estimated parameters. The work explores various theoretical frameworks and practical algorithms designed to overcome these obstacles, focusing on the trade-offs between model complexity, data availability, and estimation accuracy.

This work is recognized as a rigorous and comprehensive treatment of advanced topics in statistical estimation and inverse problems, likely appealing to researchers and graduate students in statistics, machine learning, and applied mathematics. Its focus on theoretical underpinnings and mathematical analysis suggests a dense, specialist text that contributes to the understanding of complex estimation challenges in high-dimensional settings. The book is expected to provide a solid theoretical basis for developing and analyzing new algorithms in these areas.