Asymptotics

CLASS INFO

• Semester: Fall, 2026
• Class time/ Class room: / Mirae Building
• Text book:
  • van der Vaart — Asymptotic Statistics
  • Billingsley — Convergence in Measure
  • Pollard — Empirical Processes: Theory and Applications
• Course Description: This course introduces weak convergence of random elements in metric spaces, with emphasis on probability measures on function spaces such as C[0,1]. Wiener measure appears as the canonical Gaussian limit. The second half of the course develops empirical process theory, including VC classes, uniform laws of large numbers, and stochastic equicontinuity leading to functional central limit theorems.
  
  Policy on Proofs: Portmanteau lemma and Prokhorov theorem will be stated and used as black-box tools. The focus is on applications to empirical processes rather than measure-theoretic compactness proofs.

CONTENTS

• [Week 1] Stochastic Convergence
  • Course materials (link)
• [Week 2] Delta Method
  • Course materials (link)
• [Week 3] Basic of M-Estimator
  • Course materials (link)
• [Week 4] Probability on Metric Space
  • Course materials (link)
• [Week 5] Empirical Process
  • Course materials (link)
• [Week 6] Applications
  • Course materials (link)