\BOOKMARK [1][-]{section.1}{Introduction}{} \BOOKMARK [2][-]{subsection.1.1}{Motivation and Some Background}{section.1} \BOOKMARK [2][-]{subsection.1.2}{The Statistical Problems and Methodology}{section.1} \BOOKMARK [2][-]{subsection.1.3}{An Overview of the Estimators and the Results}{section.1} \BOOKMARK [2][-]{subsection.1.4}{Outline}{section.1} \BOOKMARK [1][-]{section.2}{The Estimators and Central Limit Theorems}{} \BOOKMARK [1][-]{section.3}{The Model Selection Problem}{} \BOOKMARK [2][-]{subsection.3.1}{Analysis of the Variance Term}{section.3} \BOOKMARK [2][-]{subsection.3.2}{The Approximation Error for Besov Type Smooth Functions}{section.3} \BOOKMARK [2][-]{subsection.3.3}{Rate of Convergence for Smooth Functions Via Splines}{section.3} \BOOKMARK [2][-]{subsection.3.4}{About the Critical Mesh}{section.3} \BOOKMARK [1][-]{section.4}{Minimax Risk of Estimation for Smooth L\351vy Densities}{} \BOOKMARK [1][-]{section.5}{A Data-Driven Selection Method and Adaptability}{} \BOOKMARK [1][-]{section.6}{An Example: Estimation of Variance Gamma Processes.}{} \BOOKMARK [2][-]{subsection.6.1}{The Model}{section.6} \BOOKMARK [2][-]{subsection.6.2}{The Simulation Procedure}{section.6} \BOOKMARK [2][-]{subsection.6.3}{The Numerical Results}{section.6} \BOOKMARK [1][-]{section*.3}{Appendix A: Technical Proofs}{} \BOOKMARK [1][-]{section*.5}{Appendix B: Figures}{} \BOOKMARK [1][-]{section*.7}{References}{}