Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

GMM and M Estimation under Network Dependence

Yuya Sasaki

Abstract

This paper presents GMM and M estimators and their asymptotic properties for network-dependent data. To this end, I build on Kojevnikov, Marmer, and Song (KMS, 2021) and develop a novel uniform law of large numbers (ULLN), which is essential to ensure desired asymptotic behaviors of nonlinear estimators (e.g., Newey and McFadden, 1994, Section 2). Using this ULLN, I establish the consistency and asymptotic normality of both GMM and M estimators. For practical convenience, complete estimation and inference procedures are also provided.

GMM and M Estimation under Network Dependence

Abstract

This paper presents GMM and M estimators and their asymptotic properties for network-dependent data. To this end, I build on Kojevnikov, Marmer, and Song (KMS, 2021) and develop a novel uniform law of large numbers (ULLN), which is essential to ensure desired asymptotic behaviors of nonlinear estimators (e.g., Newey and McFadden, 1994, Section 2). Using this ULLN, I establish the consistency and asymptotic normality of both GMM and M estimators. For practical convenience, complete estimation and inference procedures are also provided.

Paper Structure

This paper contains 20 sections, 5 theorems, 46 equations.

Table of Contents

  1. Introduction
  2. The Setup
  3. Conditionally $\psi$-Dependent Processes
  4. Function Classes
  5. Uniform Law of Large Numbers
  6. M Estimation
  7. Consistency of the M Estimator
  8. Asymptotic Normality of the M Estimator
  9. Guide in Practice for M Estimation
  10. GMM Estimation
  11. Consistency of the GMM Estimator
  12. Asymptotic Normality of the GMM Estimator
  13. Guide in Practice for GMM Estimation
  14. Summary and Discussions
  15. Proofs
  16. ...and 5 more sections

Key Result

Theorem 1

If Assumptions a:kms21--a:equi are satisfied, then

Theorems & Definitions (11)

  • Definition 1: Conditional $\psi$-Dependence; KMS, Definition 2.2
  • Theorem 1: Uniform Law of Large Numbers
  • Corollary 1: Consistency of the M Estimator
  • Corollary 2: Asymptotic Normality of the M Estimator
  • Corollary 3: Consistency of the GMM Estimator
  • Corollary 4: Asymptotic Normality of the GMM Estimator
  • proof
  • proof
  • proof
  • proof
  • ...and 1 more