Journal ArticleDOI
On The Speed Of Convergence In The Central Limit Theorem Of Sequential Log-Likelihood Ratio Processes
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TLDR
In this article, under a very general dependence set-up, a rate of convergence of the randomly stopped normallocated log-I lkellihoods to standard normal varlables was shown.Abstract:
In this paper we,under a very general dependence set-up,obtaln a rate of convergence of the randomly stopped normallzed log-I lkel lhood ratlo statlstlc to standard normal varlables.Two examples are taken Into account.Non-unlform rates of convergence and bounds for Lp norms are also obtained under some qulte general condltlons.Martlngale techniques have been exploited throughout.read more
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MonographDOI
Contiguity of Probability Measures: Some Applications in Statistics
TL;DR: Asymptotic expansion and asymptotically optimal tests as discussed by the authors have been used to estimate a family of probability measures by an exponential family of probabilistic functions. But they have not yet been applied to the problem of contiguity.
Journal ArticleDOI
Exact Convergence Rates in Some Martingale Central Limit Theorems
TL;DR: In this paper, the convergence rates for martingale difference arrays are derived in central limit theorems for Martingale Difference Arrays, and it is shown that the rates which are obtained are the exact ones under the stated conditions.
Journal ArticleDOI
Large-sample theory of sequential estimation
TL;DR: In this article, it was shown that the uniform continuity condition satisfied by the statistic used is sufficient for a fixed-sample-size estimator to be valid for large-scale sequential estimation.
Journal ArticleDOI
The accuracy of the normal approximation for minimum contrast estimates
R. Michel,Johann Pfanzagl +1 more
Journal ArticleDOI
A Nonuniform Bound on the Rate of Convergence in the Martingale Central Limit Theorem
Erich Haeusler,Konrad Joos +1 more
TL;DR: In this article, a non-uniform bound on the rate of convergence to normality in the central limit theorem for martingales having finite moments of order for some δ < ∞ was obtained.