Statistical Inference for Ergodic Diffusion Processes
Statistical Inference for Ergodic Diffusion Processes

Author: Yury A. Kutoyants

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 493

ISBN-13: 144713866X

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The first book in inference for stochastic processes from a statistical, rather than a probabilistic, perspective. It provides a systematic exposition of theoretical results from over ten years of mathematical literature and presents, for the first time in book form, many new techniques and approaches.

Scientific Inference, Data Analysis, and Robustness
Scientific Inference, Data Analysis, and Robustness

Author: G. E. P. Box

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 317

ISBN-13: 1483259390

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Mathematics Research Center Symposium: Scientific Inference, Data Analysis, and Robustness focuses on the philosophy of statistical modeling, including model robust inference and analysis of data sets. The selection first elaborates on pivotal inference and the conditional view of robustness and some philosophies of inference and modeling, including ideas on modeling, significance testing, and scientific discovery. The book then ponders on parametric empirical Bayes confidence intervals, ecumenism in statistics, and frequency properties of Bayes rules. Discussions focus on consistency of Bayes rules, scientific method and the human brain, and statistical estimation and criticism. The book takes a look at the purposes and limitations of data analysis, likelihood, shape, and adaptive inference, statistical inference and measurement of entropy, and the robustness of a hierarchical model for multinomials and contingency tables. Topics include numerical results for contingency tables and robustness, multinomials, flattening constants, and mixed Dirichlet priors, entropy and likelihood, and test as measurement of entropy. The selection is a valuable reference for researchers interested in robust inference and analysis of data sets.

On the Statistical Estimation of Diffusion Processes - A Survey
On the Statistical Estimation of Diffusion Processes - A Survey

Author: Rubens Penha Cysne

Publisher:

Published: 2014

Total Pages: 30

ISBN-13:

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Data available on continuous-time diffusions are always sampled discretely in time. In most cases, the likelihood function of the observations is not directly computable. This survey covers a sample of the statistical methods that have been developed to solve this problem. We concentrate on some recent contributions to the literature based on three different approaches to the problem: an improvement of the Euler-Maruyama discretization scheme, the use of Martingale Estimating Functions and the application of Generalized Method of Moments (GMM).