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Since sup√T −pmax∥θ−θ0∥F ≤c ∥θ − θ0∥F = op(1), condition (S.4.9) holds if ∥∂vec(IT (θ))/∂θT∥F (T −pmax) = Op(1) uniformly for θ ⊂ Θ

By mean value inequality, sup√T −pmax∥θ−θ0∥F ≤c ∥IT (θ) − IT (θ0)∥F (T − pmax) ≤ sup√T −pmax∥θ−θ0∥F ≤c ∥θ−θ0∥F sup√T −pmax∥θ−θ0∥F ≤c ∥∂vec(IT (θ))/∂θT∥F T − pmax · 1980

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Mixture Matrix-valued Autoregressive Model

stat.ME · 2023-12-11 · unverdicted · novelty 6.0

Proposes MMAR model using EM algorithm for regime shifts in matrix time series, deriving consistency and asymptotic normality.

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  • Mixture Matrix-valued Autoregressive Model stat.ME · 2023-12-11 · unverdicted · none · ref 11

    Proposes MMAR model using EM algorithm for regime shifts in matrix time series, deriving consistency and asymptotic normality.