Mu Zhu · 2023
Abstract This chapter begins by pointing out that, while we don’t usually care much about model parameters that don’t have intrinsic scientific meaning, it is often important for us to quantify how much uncertainty we have about those that do. This leads to the more intricate inferential task of interval estimation. Students will learn about how Bayesian credible intervals and frequentist confidence intervals can be constructed in principle, why the latter is often hard, and the historic significance of the Student’s t-distribution. Two methods, based respectively on the likelihood ratio and the bootstrap, are then introduced.
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Bruce J. Chalmer · 2020
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Masahito Hayashi · 2006
Summary. We formulate two types of extensions of the large deviation theory initiated by Bahadur in a non-regular setting. One can be regarded as a bound of the point estimation, the other can be regarded as the limit of a bound of the interval estimation. Both coincide in the regular case, but do not necessarily coincide in a non-regular case. Using the limits of relative Rényi entropies, we derive their upper bounds and give a necessary and sufficient condition for the coincidence of the two upper bounds. We also discuss the attainability of these two bounds in several non-regular location shift families.
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Pradip Kumar Sahu, Santi Ranjan Pal, Ajit Das · 2015
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World Scientific lecture notes in economics and policy · 2024
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Cagnone, Silvia · AMS Campus - AlmaDL · 2013
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G. P. Beaumont · 1980
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J. Rissanen · Cambridge University Press eBooks · 2012
Now that we know how to estimate real-valued parameters optimally the question arises of how confident we can be in the estimated result, which requires infinite precision numbers. It is clear that if we repeat the estimation on a new set of data, generated by the same physical machinery, the result will not be the same. It seems that the model class is too rich for the amount of data we have. After all, if we fit Bernoulli models to a binary string of length n, there cannot be more than 2n properties in the data that we can learn, even if no two strings have a common property. And yet the model class has a continuum of parameter values, each representing a property.
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2014
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2014
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Sujit K. Sahu · 2024
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Joshua C. C. Chan, Gary Koop, Dale J. Poirier et al. · Cambridge University Press eBooks · 2019
Bayesian Econometric Methods examines principles of Bayesian inference by posing a series of theoretical and applied questions and providing detailed solutions to those questions. This second edition adds extensive coverage of models popular in finance and macroeconomics, including state space and unobserved components models, stochastic volatility models, ARCH, GARCH, and vector autoregressive models. The authors have also added many new exercises related to Gibbs sampling and Markov Chain Monte Carlo (MCMC) methods. The text includes regression-based and hierarchical specifications, models based upon latent variable representations, and mixture and time series specifications. MCMC methods are discussed and illustrated in detail - from introductory applications to those at the current research frontier - and MATLAB® computer programs are provided on the website accompanying the text. Suitable for graduate study in economics, the text should also be of interest to students studying statistics, finance, marketing, and agricultural economics.
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Paul H. Garthwaite, Ian T. Jolliffe, Byron Jones · 2002
Abstract In Chapters 2 and 3 we discussed point estimation at some length. However, as was noted in Chapter 1, a point estimate on its own is of little use—some measure of its precision is also necessary. This leads naturally to the idea of interval estimation, which is of great practical importance. Nevertheless, we devote less space in this book to interval estimation than to either point estimation or hypothesis testing. This is because the theory underlying interval estimation is closely related to that already covered for point estimation and hypothesis testing, and the theory is most conveniently developed in these latter contexts. In fact, there is a close relationship between interval estimation and hypothesis testing, so that many of the ideas of hypothesis testing carry over directly to interval estimation; we show this later for some of the more useful ideas. The approach used in most of this chapter is known as the frequentist approach.
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2017
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Ole J. Forsberg · 2024
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Lawrence B.Mohr · 1990
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Hafiz Alshammery, M. Nafi Toksöz · 1998
PreviousNext No AccessSEG Technical Program Expanded Abstracts 1998Interval attenuation estimationAuthors: Hafiz AlshammeryM. N. ToksozHafiz AlshammeryEarth Resources Lab, MIT and M. N. ToksozEarth Resources Lab, MIThttps://doi.org/10.1190/1.1820659 SectionsAboutPDF/ePub ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InRedditEmail Permalink: https://doi.org/10.1190/1.1820659FiguresReferencesRelatedDetails SEG Technical Program Expanded Abstracts 1998ISSN (print):1052-3812 ISSN (online):1949-4645Copyright: 1998 Pages: 2092 publication data© 1998 Copyright © 1998 Society of Exploration GeophysicistsPublisher:Society of Exploration Geophysicists HistoryPublished: 06 Jan 2005 CITATION INFORMATION Hafiz Alshammery and M. N. Toksoz, (1998), "Interval attenuation estimation," SEG Technical Program Expanded Abstracts : 988-991. https://doi.org/10.1190/1.1820659 Plain-Language Summary PDF DownloadLoading ...
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2023
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Siddhartha Srivastava (8084513), Patrick C. Kinnunen (22513514), Zhenlin Wang (675456) et al. · Figshare · 2025
Derivation of local-quadratic uncertainty bounds and parameter estimates for the inferred PDE models. (PDF)
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Nitis Mukhopadhyay · 2020
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