Existence, consistency and computer simulation for selected variants of minimum distance estimators

Kus, V.; Morales, Domingo; Hrabáková, Jitka; Frýdlová, Iva

doi:10.14736/kyb-2018-2-0336

Cited by 1 publication

(4 citation statements)

References 13 publications

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“…). But V (M, P ) and V (M, Q) are calculated in ( 29) and (30). Hence we have D RJS (P, Q; π) ≥ 1 2 φ (1)V (P, Q) 2 .…”

Section: Bounds For Jsd Using the Decompositionmentioning

confidence: 96%

“…The notations and definitions, including Chan and Darwiche metric, φ-divergences, JSD, and reversed JSD, are presented in Section 2. Here JSD and reversed JSD are introduced by the notion of blending in [29]. The Pinsker inequality and reverse Pinsker inequality, see [41] are used for the first upper and lower bounds for JSD in terms of the variation distance in Section 3.…”

Section: Organization Of the Papermentioning

confidence: 99%

“…and similarly for D KL (Q, M ) with Q replacing P . When we insert the rightmost expressions in ( 29) and (30) in the right hand sides of the bounds on D KL (P, M ) and D KL (Q, M ) above, respectively, we obtain by the same computation as above the right hand side inequality in (27).…”

Section: Applications Of Pinsker and Reverse Pinsker Inequalitiesmentioning

confidence: 99%

“…P r o o f . We apply first (37) in the two terms in D JS (P, Q) and then ( 29) and (30) in the two KL-divergences to obtain a lower bound, where we set π = 1 2 .…”

Section: Lower Bounds For Jsd By Refinements Of Pinsker's Inequalitymentioning

confidence: 99%

See 3 more Smart Citations

On the Jensen-Shannon divergence and the variation distance for categorical probability distributions

Corander¹,

Remes²,

Koski³

2022

Kybernetika

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We establish a decomposition of the Jensen-Shannon divergence into a linear combination of a scaled Jeffreys' divergence and a reversed Jensen-Shannon divergence. Upper and lower bounds for the Jensen-Shannon divergence are then found in terms of the squared (total) variation distance. The derivations rely upon the Pinsker inequality and the reverse Pinsker inequality. We use these bounds to prove the asymptotic equivalence of the maximum likelihood estimate and minimum Jensen-Shannon divergence estimate as well as the asymptotic consistency of the minimum Jensen-Shannon divergence estimate. These are key properties for likelihood-free simulator-based inference.

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“…). But V (M, P ) and V (M, Q) are calculated in ( 29) and (30). Hence we have D RJS (P, Q; π) ≥ 1 2 φ (1)V (P, Q) 2 .…”

Section: Bounds For Jsd Using the Decompositionmentioning

confidence: 96%

Section: Organization Of the Papermentioning

confidence: 99%

Section: Applications Of Pinsker and Reverse Pinsker Inequalitiesmentioning

confidence: 99%

“…P r o o f . We apply first (37) in the two terms in D JS (P, Q) and then ( 29) and (30) in the two KL-divergences to obtain a lower bound, where we set π = 1 2 .…”

Section: Lower Bounds For Jsd By Refinements Of Pinsker's Inequalitymentioning

confidence: 99%

See 2 more Smart Citations

On the Jensen-Shannon divergence and the variation distance for categorical probability distributions

Corander¹,

Remes²,

Koski³

2022

Kybernetika

View full text Add to dashboard Cite

show abstract

Existence, consistency and computer simulation for selected variants of minimum distance estimators

Cited by 1 publication

References 13 publications

On the Jensen-Shannon divergence and the variation distance for categorical probability distributions

On the Jensen-Shannon divergence and the variation distance for categorical probability distributions

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