The Experts below are selected from a list of 23973 Experts worldwide ranked by ideXlab platform
Bin Yang - One of the best experts on this subject based on the ideXlab platform.
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Bayesian Estimation for Nonstandard Loss Functions Using a Parametric Family of Estimators
IEEE Transactions on Signal Processing, 2012Co-Authors: Stefan Uhlich, Bin YangAbstract:Bayesian estimation with other loss functions than the standard hit-or-miss loss or the quadratic loss often yields optimal Bayesian estimators (OBEs) that can only be formulated as optimization problems and which have to be solved for each new observation. The contribution of this paper is to introduce a new Parametric Family of estimators to circumvent this problem. By restricting the estimator to lie in this Family, we split the estimation problem into two parts: In a first step, we have to find the best estimator with respect to the Bayes risk for a given nonstandard loss function, which has to be done only once. The second step then calculates the estimate for an observation using importance sampling. The computational complexity of this second step is therefore comparable to that of an MMSE estimator if the MMSE estimator also uses Monte Carlo integration. We study the proposed Parametric Family using two examples and show that the estimator Family gives for both a good approximation of the OBE.
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a Parametric Family of bayesian estimators for non standard loss functions
European Signal Processing Conference, 2010Co-Authors: Stefan Uhlich, Bin YangAbstract:This paper introduces a new Parametric Family of Bayesian estimators. As the estimation with non-standard loss functions can often only be stated as an optimization problem which has to be solved for each new observation, it is advantageous to use such a Parametric Family. We proof that many well known estimators are included in our Family. Among them are the MMSE and MAP estimator as well as the optimal Bayesian estimator (OBE) under LINEX loss. By restricting the estimator to lie in this Family, we split the estimation problem into two parts: In a first step, we have to find the best estimator with respect to the Bayes risk for a given loss function, which has to be done only once. The second step then calculates the estimate for a given observation. We demonstrate the usefulness of the proposed Parametric Family in an example.
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EUSIPCO - A Parametric Family of Bayesian estimators for non-standard loss functions
2010Co-Authors: Stefan Uhlich, Bin YangAbstract:This paper introduces a new Parametric Family of Bayesian estimators. As the estimation with non-standard loss functions can often only be stated as an optimization problem which has to be solved for each new observation, it is advantageous to use such a Parametric Family. We proof that many well known estimators are included in our Family. Among them are the MMSE and MAP estimator as well as the optimal Bayesian estimator (OBE) under LINEX loss. By restricting the estimator to lie in this Family, we split the estimation problem into two parts: In a first step, we have to find the best estimator with respect to the Bayes risk for a given loss function, which has to be done only once. The second step then calculates the estimate for a given observation. We demonstrate the usefulness of the proposed Parametric Family in an example.
Stefan Uhlich - One of the best experts on this subject based on the ideXlab platform.
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Bayesian Estimation for Nonstandard Loss Functions Using a Parametric Family of Estimators
IEEE Transactions on Signal Processing, 2012Co-Authors: Stefan Uhlich, Bin YangAbstract:Bayesian estimation with other loss functions than the standard hit-or-miss loss or the quadratic loss often yields optimal Bayesian estimators (OBEs) that can only be formulated as optimization problems and which have to be solved for each new observation. The contribution of this paper is to introduce a new Parametric Family of estimators to circumvent this problem. By restricting the estimator to lie in this Family, we split the estimation problem into two parts: In a first step, we have to find the best estimator with respect to the Bayes risk for a given nonstandard loss function, which has to be done only once. The second step then calculates the estimate for an observation using importance sampling. The computational complexity of this second step is therefore comparable to that of an MMSE estimator if the MMSE estimator also uses Monte Carlo integration. We study the proposed Parametric Family using two examples and show that the estimator Family gives for both a good approximation of the OBE.
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a Parametric Family of bayesian estimators for non standard loss functions
European Signal Processing Conference, 2010Co-Authors: Stefan Uhlich, Bin YangAbstract:This paper introduces a new Parametric Family of Bayesian estimators. As the estimation with non-standard loss functions can often only be stated as an optimization problem which has to be solved for each new observation, it is advantageous to use such a Parametric Family. We proof that many well known estimators are included in our Family. Among them are the MMSE and MAP estimator as well as the optimal Bayesian estimator (OBE) under LINEX loss. By restricting the estimator to lie in this Family, we split the estimation problem into two parts: In a first step, we have to find the best estimator with respect to the Bayes risk for a given loss function, which has to be done only once. The second step then calculates the estimate for a given observation. We demonstrate the usefulness of the proposed Parametric Family in an example.
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EUSIPCO - A Parametric Family of Bayesian estimators for non-standard loss functions
2010Co-Authors: Stefan Uhlich, Bin YangAbstract:This paper introduces a new Parametric Family of Bayesian estimators. As the estimation with non-standard loss functions can often only be stated as an optimization problem which has to be solved for each new observation, it is advantageous to use such a Parametric Family. We proof that many well known estimators are included in our Family. Among them are the MMSE and MAP estimator as well as the optimal Bayesian estimator (OBE) under LINEX loss. By restricting the estimator to lie in this Family, we split the estimation problem into two parts: In a first step, we have to find the best estimator with respect to the Bayes risk for a given loss function, which has to be done only once. The second step then calculates the estimate for a given observation. We demonstrate the usefulness of the proposed Parametric Family in an example.
Li Zhigang - One of the best experts on this subject based on the ideXlab platform.
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A Parametric Family of Quartic Thue Equations
Advances in Mathematics, 2010Co-Authors: Li ZhigangAbstract:In this paper,we give all primitive solutions of a parameterized Family of quartic Thue equations x~4- 4cx~3y +(6c + 2)x~2y~2 + 4cxy~3 + y~4 = 96c + 169,c 0.
Tarik Yalcin - One of the best experts on this subject based on the ideXlab platform.
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inequality measurement for ordered response health data
Journal of Health Economics, 2008Co-Authors: Ramses Abul H Naga, Tarik YalcinAbstract:Because self-reported health status [SRHS] is an ordered response variable, inequality measurement for SRHS data requires a numerical scale for converting individual responses into a summary statistic. The choice of scale is however problematic, since small variations in the numerical scale may reverse the ordering of a given pair of distributions of SRHS data in relation to conventional inequality indices such as the variance. This paper introduces a Parametric Family of inequality indices, founded on an inequality ordering proposed by Allison and Foster [Allison, R.A., Foster, J., 2004. Measuring health inequalities using qualitative data. Journal of Health Economics 23, 505-524], which satisfy a suitable invariance property with respect to the choice of numerical scale. Several key members of the Parametric Family are also derived, and an empirical application using data from the Swiss Health Survey illustrates the proposed methodology.
Juan L. Varona - One of the best experts on this subject based on the ideXlab platform.
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RECURSIVE FORMULAS RELATED TO THE SUMMATION
2008Co-Authors: Manuel Benito, Juan L. VaronaAbstract:For positive integers n, let (n) be the Mobius function, and M(n) its sum M(n) = P n=1 (k). We nd some identities and recursive formulas for computing M(n); in particular, we present a two-Parametric Family of recursive formulas.
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Recursive formulas related to the summation of the mobius function
The Open Mathematics Journal, 2008Co-Authors: Manuel Benito, Juan L. VaronaAbstract:For positive integers n, let μ(n) be the Mobius function, and M(n) its sum M(n) = Pn k=1 μ(k). We find some identities and recursive formulas for computing M(n); in particular, we present a two-Parametric Family of recursive formulas.