Convergence rates in the central limit theorem for weighted sums of Bernoulli random fields

Davide Giraudo (1)

1 Fakultät für Mathematik [Bochum]

We prove moment inequalities for a class of functionals of i.i.d. random fields. We then derive rates in the central limit theorem for weighted sums of such randoms fields via an approximation by $m$-dependent random fields.

Mots clés: Central limit theorem for spatial random fields; Rates of convergence; Bernoulli process

Domaines: Statistiques [math.ST]; Probabilités [math.PR]

Davide Giraudo. Convergence rates in the central limit theorem for weighted sums of Bernoulli random fields. 2018. ⟨hal-01491148v2⟩