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Showing 1 to 20 of 45 for “"Empirical Bayes"”.
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Some parametric empirical Bayes techniques
This thesis considers two distinct aspects of the empirical Bayes decision problem. The first aspect considered is the problem or point estimation and hypothesis testing. The second aspect considered is that of estimating the prior distribution and then the estimation of posterior distribution and …
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Generalized Empirical Bayes: Theory, Methodology, and Applications
The two key issues of modern Bayesian statistics are: (i) establishing a principled approach for \textit{distilling} a statistical prior distribution that is \textit{consistent} with the given data from an initial believable scientific prior; and (ii) development of a \textit{consolidated} …
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Empirical Bayes methods in time series analysis
… vary randomly from experiment to experiment, the Empirical Bayes method often leads to estimators which have smaller mean squared errors than the classical estimators. Suppose there is an unobservable random variable θ, where θ ~ G(θ), usually called a prior distribution. The Bayes estimator of θ …
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Empirical Bayes procedures in time series analysis
Empirical Bayes analysis concerns the analysis of data which occur in similar recurring situations. The parameters involved in the recurring situations are generated independently from an unknown probability distribution G(θ). In many situations it is possible to use the estimates of all of the …
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Transformers as Empirical Bayes Estimators The Poisson Model
… In Context Learning (ICL) in the setting of Empirical Bayes for the Poison Model. On the theoretical side, we demonstrate the expressibility of transformers by formulating a way to approximate the Robbins estimator, the first empirical Bayes estimator for the Poisson model. On the empirical …
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Empirical Bayes procedures in time series regression models
In this dissertation empirical Bayes estimators for the coefficients in time series regression models are presented. Due to the uncontrollability of time series observations, explanatory variables in each stage do not remain unchanged. A generalization of the results of O'Bryan and Susarla is …
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Contributions to the Analysis of Experiments Using Empirical Bayes Techniques
… statistical model is a difficult step in the Bayesian approach to the design and analysis of experiments. Here we address this difficulty by proposing the use of functional priors and then by working out important details for three and higher level experiments. One of the challenges presented …
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Empirical Bayes via ERM and Rademacher complexities: the Poisson model
We consider the problem of empirical Bayes estimation for (multivariate) Poisson means. Existing solutions that have been shown theoretically optimal for minimizing the regret (excess risk over the Bayesian oracle that knows the prior) have several shortcomings. For example, the classical Robbins …
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Empirical Bayes estimators for the cross-product ratio of 2x2 contingency tables
… knowledge of the exact prior distribution the Bayes estimator cannot be obtained. However, as long as independent repetitions of the experiment occur, the empirical Bayes approach can then be applied. A general strategy underlying the empirical Bayes estimator consists of finding the Bayes …
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Improved Estimators Under Squared Error Loss (Stein Estimator, Decision Theory, Empirical Bayes, Quadratic, Robust Estimation)
Much work on the James-Stein (1964) estimator or an improved estimator under squared error loss has been done with the assumption of independently identically distributed normal errors.
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Investigation of the rate of convergence in the two sample nonparametric empirical Bayes approach to an estimation problem
… one. With the risk defined in the usual way the Bayes decision function is the expected value of θ given that X = x. Since the distributions are unknown, the use of the two sample nonparametric empirical Bayes decision function is proposed. With the regret defined in the usual way it can be shown …
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A comparison of a supplementary sample non-parametric empirical Bayes estimator with the classical estimator in a quality control situation
… that of a supplementary sample non-parametric empirical Bayes estimator in detecting an out-of-control situation arising in statistical quality control work. The investigation was accomplished through Monte Carlo simulation on the IBM-7040/1401 system at the Virginia Polytechnic Institute …
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Stochastic Models for Triangular Tables with Applications to Cohort Data and Claims Reserving
… Ladder Linear Model" is extended to encompass Bayesian, empirical Bayes and dynamic estimation. The empirical Bayes results are given a credibility theory interpretation, and the advantages and disadvantages of the various approaches are highlighted. Finally, the methods are extended to …
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Impact of Ignoring Nested Data Structures on Ability Estimation
… which are random effect predictions known as empirical Bayes estimates in the one-parameter IRT / Rasch model. The literature on the impact of complex survey design on latent trait models is mixed and there is no "best practice" established regarding how to handle this situation. A simulation …
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Some theoretical and applied results concerning item response theory model estimation
… Theory (IRT) folklore that under the usual empirical Bayes unidimensional IRT modeling approach, the posterior distribution of examinee ability given test response is approximately normal for a long test. Under very general non-parametric assumptions, we make this claim rigorous for a broad …
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Hierarchical modelling of multivariate survival data
… and Oakes (1986, 1989). Both approximate Bayesian and maximum likelihood estimation in these models is investigated via simulation. Predicting a component of a response vector on the basis of other components of the response and other vectors is also studied, using Bayes and empirical …
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On the Optimality of Several Algorithms on Polynomial Regression of Empicial Bayes Poisson Model
The empirical Bayes estimator for the Poisson mixture model in [1], [2] has been an important problem studied for the past 70 years. In this thesis, we investigate extensions of this problem to estimating polynomial functions of the Poisson parameter rather than just the parameter itself. We …
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Simultaneous estimation approaches to large-scale multivariate regression
… decision problem. In Chapter 2, we propose an empirical Bayes-based approach where the prior distribution of unknown parameters is estimated nonparametrically from the data. Unlike existing methods, the proposed method does not assume any structure of parameters. In Chapter 3, we propose a …
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Bayesian Adjustment for Multiplicity
<p>This thesis is about Bayesian approaches for handling multiplicity. It considers three main kinds of multiple-testing scenarios: tests of exchangeable experimental units, tests for variable inclusion in linear regresson models, and tests for conditional independence in jointly normal vectors. …
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'Ex-ante' asset allocation strategies for global index portfolios
… market. Effectively, the principal focus lies in empirically assessing the extent of inter~temporal instability in the inputs to theglobal portfolio optimization problem and in developing appropriate multivariate estimation procedures that aim to assist investors in achieving superior out of …
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