An Autoregressive Model for Time Series of Random Objects: Appendix B. Proofs

Table of Links

Abstract and 1. Introduction

2. Preliminaries

3. The GAR(1) Model

3.1. Model and Stationary Solution

3.2. Identifability

4. Estimation of model parameters and 4.1. Fréchet mean

4.2. Concentration parameter

5. Testing for the absence of serial dependence

6. Numerical experiments

6.1. R with multiplicative noise

6.2. Univariate distributions with a density

6.3. SPD Matrices

7. Application

8. Acknowledgement

Appendix A. General results in Hadamard spaces

Appendix B. Proofs

Reference

Appendix B. Proofs

Consistency of the mean estimator

Plugin this bound in the infinite sum, this gives

Using this bound in the sum gives

Appendix B.1. Uniform convergence of LT

Again using that Ω is bounded, the average is also bounded and we obtain the desired result.