ISSN:
1572-9230
Keywords:
Speed of convergence
;
CLT
;
log-likelihood ratio process
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Let $$\bigcirc H$$ , the parameter space, be an open subset ofR k ,k⩾1. For each $$\theta \in \bigcirc H$$ , let the r.v.'sX n ,n=1, 2,... be defined on the probability space (X, ℱP θ) and take values in (S,S,L) whereS is a Borel subset of a Euclidean space andL is the σ-field of Borel subsets ofS. Forh∈R k and a sequence of p.d. normalizing matrices ∂ n = ∂ n k × k (θ0 set θ n * = θ* = θ0 + ∂ n h, where θ0 is the true value of θ, such that θ*, $$\theta _0 \in \bigcirc H$$ . Let Δ n (θ*, θ*)( be the log-likelihood ratio of the probability measure $$P_{n\theta ^* } $$ with respect to the probability measure $$P_{n\theta _0 } $$ , whereP nθ is the restriction ofP θ over ℱ n = σ(X 1,X 2,...,X n . In this paper we, under a very general dependence setup obtain a rate of convergence of the normalized log-likelihood ratio statistic to Standard Normal Variable. Two examples are taken into account.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01049167
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