Asymptotic theory of sequential estimation: Differential geometrical approach

DOI10.1214/aos/1176348131zbMath0737.62067OpenAlexW2058847744MaRDI QIDQ1175393

Ichi Okamoto, Shun-ichi Amari, Kei Takeuchi

Publication date: 25 June 1992

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1176348131

zbMATH Keywords

stopping timesconformal transformationexponential curvaturestatistical curvaturecovariance stabilizationexponential families of stochastic processeshigher order asymptotic properties of sequential estimation proceduresmultiparameter curved exponential familiesnoncurved exponential familiessecond-order efficient sequential estimation procedure

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Sequential estimation (62L12)

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On the divergence of 1-conformally flat statistical manifolds ⋮ Gradient systems in view of information geometry ⋮ Conformal implementation of the projective equivalence over statistical manifolds ⋮ Geometry of \(q\)-exponential family of probability distributions ⋮ Informative fractal dimension associated with nonmetricity in information geometry ⋮ On the α-connections and the α-conformal equivalence on statistical manifolds ⋮ The bhattacharyya type bound foe the asymptotic variance and the sequential discretized likelihood estimation procedure ⋮ Unnamed Item ⋮ Discussion on “Sequential Estimation for Time Series Models” by T. N. Sriram and Ross Iaci ⋮ Conformal geometry of sequential test in multidimensional curved exponential family ⋮ Conformal Geometry of Statistical Manifold with Application to Sequential Estimation

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