Asymptotically efficient recursive estimation for incomplete data models using the observed information

Metrika ◽  
1998 ◽  
Vol 47 (1) ◽  
pp. 119-145 ◽  
Author(s):  
Tobias Rydén
Keyword(s):  
Incomplete Data ◽  
Data Models ◽  
Recursive Estimation ◽  
Observed Information ◽  
Asymptotically Efficient

scholarly journals Fast, Asymptotically Efficient, Recursive Estimation in a Riemannian Manifold

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 1021 ◽  
Author(s):  
Jialun Zhou ◽  
Salem Said
Keyword(s):  
Riemannian Manifold ◽  
Rate Of Convergence ◽  
Statistical Parameter ◽  
Recursive Estimation ◽  
Numerical Application ◽  
Stochastic Optimisation ◽  
Asymptotic Rate ◽  
Fisher Information Metric ◽  
Convexity Assumptions ◽  
Asymptotically Efficient

Stochastic optimisation in Riemannian manifolds, especially the Riemannian stochastic gradient method, has attracted much recent attention. The present work applies stochastic optimisation to the task of recursive estimation of a statistical parameter which belongs to a Riemannian manifold. Roughly, this task amounts to stochastic minimisation of a statistical divergence function. The following problem is considered: how to obtain fast, asymptotically efficient, recursive estimates, using a Riemannian stochastic optimisation algorithm with decreasing step sizes. In solving this problem, several original results are introduced. First, without any convexity assumptions on the divergence function, we proved that, with an adequate choice of step sizes, the algorithm computes recursive estimates which achieve a fast non-asymptotic rate of convergence. Second, the asymptotic normality of these recursive estimates is proved by employing a novel linearisation technique. Third, it is proved that, when the Fisher information metric is used to guide the algorithm, these recursive estimates achieve an optimal asymptotic rate of convergence, in the sense that they become asymptotically efficient. These results, while relatively familiar in the Euclidean context, are here formulated and proved for the first time in the Riemannian context. In addition, they are illustrated with a numerical application to the recursive estimation of elliptically contoured distributions.

Estimating Expected Value of Sample Information for Incomplete Data Models Using Bayesian Approximation

2011 ◽  
Vol 31 (6) ◽  
pp. 839-852 ◽  
Author(s):  
Samer A. Kharroubi ◽  
Alan Brennan ◽  
Mark Strong
Keyword(s):  
Monte Carlo ◽  
Incomplete Data ◽  
Bayesian Updating ◽  
Expected Value ◽  
Data Models ◽  
Mcmc Methods ◽  
Approximation Formula ◽  
Posterior Density ◽  
Sample Information ◽  
Bayesian Approximation

Expected value of sample information (EVSI) involves simulating data collection, Bayesian updating, and reexamining decisions. Bayesian updating in incomplete data models typically requires Markov chain Monte Carlo (MCMC). This article describes a revision to a form of Bayesian Laplace approximation for EVSI computation to support decisions in incomplete data models. The authors develop the approximation, setting out the mathematics for the likelihood and log posterior density function, which are necessary for the method. They compare the accuracy of EVSI estimates in a case study cost-effectiveness model using first- and second-order versions of their approximation formula and traditional Monte Carlo. Computational efficiency gains depend on the complexity of the net benefit functions, the number of inner-level Monte Carlo samples used, and the requirement or otherwise for MCMC methods to produce the posterior distributions. This methodology provides a new and valuable approach for EVSI computation in health economic decision models and potential wider benefits in many fields requiring Bayesian approximation.

U-statistics with conditional kernels for incomplete data models

2015 ◽  
Vol 69 (2) ◽  
pp. 271-302
Author(s):  
Ao Yuan ◽  
Mihai Giurcanu ◽  
George Luta ◽  
Ming T. Tan
Keyword(s):  
Incomplete Data ◽  
Data Models ◽  
U Statistics
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