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Conformal geometry of statistical manifold with application to sequential estimation
Affi ne connections Curved exponential family Hyperboloid dis-tribution Information geometry Projective transformation Riemannian metric Space of constant curvature Totally umbilic von Mises-Fisher distribution
2011/3/22
We present a geometrical method for analyzing sequential estimating procedures. It is based on the design principle of the second-order efficient sequential estimation provided in Okamoto, Amari and T...
Robust Estimation through Schoenberg transformations
Correspondence Analysis Euclidean distances Huber func-tion Huygens principles M-estimators Schoenberg transformations Tukey bisquare
2011/3/24
Schoenberg transformations, mapping Euclidean configurations into Euclidean configurations, define in turn a transformed inertia, whose minimization produces robust location estimates. The procedure o...
Interval Estimation for Messy Observational Data
Bayesian analysis bias confounding epidemiology
2010/10/14
We review some aspects of Bayesian and frequentist interval estimation, focusing first on their relative strengths and weaknesses when used in "clean" or "textbook" contexts. We then turn attention to...
Filtering and parameter estimation for a jump stochastic process with discrete observations
Filtering parameter estimation discrete observations
2009/3/19
A compound Poisson process is considered. We estimate the current position of the stochastic process based on past discrete-time observations (non-linear discrete filtering problem) in Bayesian settin...