Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Quasi-Akaike information criterion of structural equation modeling with latent variables for diffusion processes

Shogo Kusano, Masayuki Uchida

Abstract

We consider a model selection problem for structural equation modeling (SEM) with latent variables for diffusion processes based on high-frequency data. First, we propose the quasi-Akaike information criterion of the SEM and study the asymptotic properties. Next, we consider the situation where the set of competing models includes some misspecified parametric models. It is shown that the probability of choosing the misspecified models converges to zero. Furthermore, examples and simulation results are given.

Quasi-Akaike information criterion of structural equation modeling with latent variables for diffusion processes

Abstract

We consider a model selection problem for structural equation modeling (SEM) with latent variables for diffusion processes based on high-frequency data. First, we propose the quasi-Akaike information criterion of the SEM and study the asymptotic properties. Next, we consider the situation where the set of competing models includes some misspecified parametric models. It is shown that the probability of choosing the misspecified models converges to zero. Furthermore, examples and simulation results are given.
Paper Structure (15 sections, 14 theorems, 267 equations, 6 figures, 1 table)

This paper contains 15 sections, 14 theorems, 267 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Notation and assumptions
  3. Qaic of sem for diffusion processes
  4. Simulation results
  5. True model
  6. Competing models
  7. Model 1
  8. Model 2
  9. Model 3
  10. Simulation results
  11. proof
  12. Appendix
  13. Proofs of Lemmas
  14. Proof of (\ref{['Y1iden']})
  15. Ergodic case

Key Result

Theorem 1

Let $m\in\{1,\cdots,M\}$. Under [A] and [B1], as $n\longrightarrow\infty$,

Figures (6)

  • Figure 1: The path diagram for the example of factor analysis.
  • Figure 2: The path diagram for the example of SEM.
  • Figure 3: The path diagram of the true model at time $t$.
  • Figure 4: The path diagram of Model 1.
  • Figure 5: The path diagram of Model 2.
  • ...and 1 more figures

Theorems & Definitions (34)

  • Remark 1
  • Remark 2
  • Theorem 1
  • Remark 3
  • Remark 4
  • Theorem 2
  • Lemma 1
  • Lemma 2
  • proof : Proofs of Lemmas \ref{['thetaprob1']}-\ref{['thetaprob2']}
  • Lemma 3
  • ...and 24 more