Estimations And Tests In Change-point Models by Pons Odile

Author:Pons, Odile
Language: eng
Format: epub
ISBN: 9789813231788
Publisher: World Scientific Publishing Company
Published: 2018-02-27T16:00:00+00:00

Denoting now

and for u in T, θT,u is the vector with components and γ0 + T−1u2, with and reversely uT,θ denotes the vector of T such that θ = θT,uT, θ.

For ɛ > 0, let there is equivalence between u belongs to T,ɛ and θT,u belongs to Vɛ(θ0).

Theorem 5.5. For every ɛ > 0 sufficiently small, as T and A tend to infinity, the probability converges to zero and

Proof. Let be the vector with components and its norm is For every η > 0 the consistency of the estimators implies that for ɛ > 0 sufficiently small

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