The Experts below are selected from a list of 291 Experts worldwide ranked by ideXlab platform
Chris Shannon - One of the best experts on this subject based on the ideXlab platform.
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Strict single crossing and the Strict spence mirrlees condition a comment on monotone comparative statics
Econometrica, 1998Co-Authors: Aaron S. Edlin, Chris ShannonAbstract:MILGROM AND SHANNON (1994) clarify the relationship between order-theoretic methods for comparative statics and more traditional differential techniques by developing relationships between the differential Spence-Mirrlees single crossing property and the order-theoretic single crossing property. Both conditions are central for monotone comparative statics analysis in a number of settings. In particular, Milgrom and Shannon show that the order-theoretic single crossing property is necessary and sufficient for the set of optimal choices to be nondecreasing in certain choice problems, and that a Strict form of the single crossing property guarantees the stronger conclusion that every selection from the set of maximizers is nondecreasing in such problems. Milgrom and Shannon assert that under appropriate conditions the Spence-Mirrlees condition is equivalent to their single crossing property, and that the Strict versions are also equivalent. In this note, however, we give counterexamples which show that their Strict single crossing property may hold even though the Strict Spence-Mirrlees condition fails. In fact, we show that the Strict single crossing property may hold even though the Strict Spence-Mirrlees condition holds only on a set of arbitrarily small measure. We also give a correct statement of the relationship between the Spence-Mirrlees condition and the single crossing property. These counterexamples explain the discrepancy between the Monotonicity conclusions that Milgrom and Shannon (1994) derive from the Strict single crossing property and the Strict Monotonicity conclusions that Edlin and Shannon (1998) derive from the Strict Spence-Mirrlees condition. In Section 3 we also use these counterexamples to illustrate the fact that the Strict single crossing property can allow both pooling and separating equilibria while the Strict Spence-Mirrlees condition eliminates the possibility of pooling equilibria. The elimination of pooling equilibria in signalling and screening models is more subtle than Edlin and Shannon's (1998) Strict Monotonicity conclusions because agents need not face a differentiable constraint.
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Strict Monotonicity in comparative statics
Journal of Economic Theory, 1998Co-Authors: Aaron S. Edlin, Chris ShannonAbstract:This note provides sufficient conditions to draw Strict monotone comparative statics conclusions in optimization problems. These results extend the lattice-theoretic results of Milgrom and Shannon (1994) by imposing a stronger differential version of the single crossing property and arguing from first- order conditions. We illustrate the importance of these results through examples involving holdup problems and optimal tax problems.
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Strict Monotonicity in Comparative Statics - eScholarship
1995Co-Authors: Aaron S. Edlin, Chris ShannonAbstract:U N I V E R S I T Y O F CALIFORNIA A T B E R K E L E Y Department of Economics Berkeley, California 94720-3880 Working Paper No. 95-238 Strict Monotonicity in Comparative Statics Aaron S. Edlin Department of Economics University of California, Berkeley and National Bureau of Economic Research Chris Shannon Department of Economics University of California, Berkeley July 1995 Key words: Strict Monotonicity, comparative statics, single crossing property JEL Classification: C60, C61, D i l , H21 Abstract This note provides sufficient conditions to draw Strict monotone comparative statics conclusions in optimization problems. These results extend the lattice-theoretic results of Milgrom and Shannon (1994) by imposing a stronger differential version of the single crossing property and arguing from first-order conditions. We illustrate the importance of these results through examples involving holdup problems and optimal tax problems. Thanks to Eric Emch, Steve Goldman, and Paul Milgrom for their comments. This work has been supported in part by the National Science Foundation under grant SBR-9321022.
Holger Dette - One of the best experts on this subject based on the ideXlab platform.
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testing Strict Monotonicity in nonparametric regression
Mathematical Methods of Statistics, 2007Co-Authors: Melanie Birke, Holger DetteAbstract:A new test for Strict Monotonicity of the regression function is proposed which is based on a composition of an estimate of the inverse of the regression function with a common regression estimate. This composition is equal to the identity if and only if the ?true? regression function is Strictly monotone, and a test based on an L2-distance is investigated. The asymptotic normality of the corresponding test statistic is established under the null hypothesis of Strict Monotonicity.
Bao-gang Hu - One of the best experts on this subject based on the ideXlab platform.
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Unsupervised ranking of multi-attribute objects based on principal curves
2016 IEEE 32nd International Conference on Data Engineering (ICDE), 2016Co-Authors: Chun-guo Li, Bao-gang HuAbstract:Unsupervised ranking faces one critical challenge in evaluation applications, that is, no ground truth is available. While PageRank and its variants show a good solution in related objects, they are applicable only for ranking from link-structure data. In this work, we focus on unsupervised ranking from multi-attribute data which is also common in evaluation tasks. To overcome the challenge, we propose five essential meta-rules for the design and assessment of unsupervised ranking approaches: scale and translation invariance, Strict Monotonicity, compatibility of linearity and nonlinearity, smoothness, and explicitness of parameter size. These meta-rules are regarded as high level knowledge for unsupervised ranking tasks. Inspired by the works in [2] and [6], we propose a ranking principal curve (RPC) model, which learns a one-dimensional manifold function to perform unsupervised ranking tasks on multi-attribute observations. Furthermore, the RPC is modeled to be a cubic Bézier curve with control points reStricted in the interior of a hypercube, complying with all the five meta-rules to infer a reasonable ranking list. With control points as model parameters, one is able to understand the learned manifold and to interpret and visualize the ranking results. Numerical experiments of the presented RPC model are conducted on two open datasets of different ranking applications. In comparison with the state-of-the-art approaches, the new model is able to show more reasonable ranking lists.
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Unsupervised Ranking of Multi-Attribute Objects Based on Principal Curves
IEEE Transactions on Knowledge and Data Engineering, 2015Co-Authors: Chun-guo Li, Bao-gang HuAbstract:Unsupervised ranking faces one critical challenge in evaluation applications, that is, no ground truth is available. When PageRank and its variants show a good solution in related objects, they are applicable only for ranking from link-structure data. In this work, we focus on unsupervised ranking from multi-attribute data which is also common in evaluation tasks. To overcome the challenge, we propose five essential meta-rules for the design and assessment of unsupervised ranking approaches: scale and translation invariance, Strict Monotonicity, compatibility of linearity and nonlinearity, smoothness, and explicitness of parameter size. These meta-rules are regarded as high level knowledge for unsupervised ranking tasks. Inspired by the works in [12] and [35], we propose a ranking principal curve (RPC) model, which learns a one-dimensional manifold function to perform unsupervised ranking tasks on multi-attribute observations. Furthermore, the RPC is modeled to be a cubic Bezier curve with control points reStricted in the interior of a hypercube, complying with all the five meta-rules to infer a reasonable ranking list. With control points as model parameters, one is able to understand the learned manifold and to interpret and visualize the ranking results. Numerical experiments of the presented RPC model are conducted on two open datasets of different ranking applications. In comparison with the state-of-the-art approaches, the new model is able to show more reasonable ranking lists.
Melanie Birke - One of the best experts on this subject based on the ideXlab platform.
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testing Strict Monotonicity in nonparametric regression
Mathematical Methods of Statistics, 2007Co-Authors: Melanie Birke, Holger DetteAbstract:A new test for Strict Monotonicity of the regression function is proposed which is based on a composition of an estimate of the inverse of the regression function with a common regression estimate. This composition is equal to the identity if and only if the ?true? regression function is Strictly monotone, and a test based on an L2-distance is investigated. The asymptotic normality of the corresponding test statistic is established under the null hypothesis of Strict Monotonicity.
Aaron S. Edlin - One of the best experts on this subject based on the ideXlab platform.
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Strict single crossing and the Strict spence mirrlees condition a comment on monotone comparative statics
Econometrica, 1998Co-Authors: Aaron S. Edlin, Chris ShannonAbstract:MILGROM AND SHANNON (1994) clarify the relationship between order-theoretic methods for comparative statics and more traditional differential techniques by developing relationships between the differential Spence-Mirrlees single crossing property and the order-theoretic single crossing property. Both conditions are central for monotone comparative statics analysis in a number of settings. In particular, Milgrom and Shannon show that the order-theoretic single crossing property is necessary and sufficient for the set of optimal choices to be nondecreasing in certain choice problems, and that a Strict form of the single crossing property guarantees the stronger conclusion that every selection from the set of maximizers is nondecreasing in such problems. Milgrom and Shannon assert that under appropriate conditions the Spence-Mirrlees condition is equivalent to their single crossing property, and that the Strict versions are also equivalent. In this note, however, we give counterexamples which show that their Strict single crossing property may hold even though the Strict Spence-Mirrlees condition fails. In fact, we show that the Strict single crossing property may hold even though the Strict Spence-Mirrlees condition holds only on a set of arbitrarily small measure. We also give a correct statement of the relationship between the Spence-Mirrlees condition and the single crossing property. These counterexamples explain the discrepancy between the Monotonicity conclusions that Milgrom and Shannon (1994) derive from the Strict single crossing property and the Strict Monotonicity conclusions that Edlin and Shannon (1998) derive from the Strict Spence-Mirrlees condition. In Section 3 we also use these counterexamples to illustrate the fact that the Strict single crossing property can allow both pooling and separating equilibria while the Strict Spence-Mirrlees condition eliminates the possibility of pooling equilibria. The elimination of pooling equilibria in signalling and screening models is more subtle than Edlin and Shannon's (1998) Strict Monotonicity conclusions because agents need not face a differentiable constraint.
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Strict Monotonicity in comparative statics
Journal of Economic Theory, 1998Co-Authors: Aaron S. Edlin, Chris ShannonAbstract:This note provides sufficient conditions to draw Strict monotone comparative statics conclusions in optimization problems. These results extend the lattice-theoretic results of Milgrom and Shannon (1994) by imposing a stronger differential version of the single crossing property and arguing from first- order conditions. We illustrate the importance of these results through examples involving holdup problems and optimal tax problems.
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Strict Monotonicity in Comparative Statics - eScholarship
1995Co-Authors: Aaron S. Edlin, Chris ShannonAbstract:U N I V E R S I T Y O F CALIFORNIA A T B E R K E L E Y Department of Economics Berkeley, California 94720-3880 Working Paper No. 95-238 Strict Monotonicity in Comparative Statics Aaron S. Edlin Department of Economics University of California, Berkeley and National Bureau of Economic Research Chris Shannon Department of Economics University of California, Berkeley July 1995 Key words: Strict Monotonicity, comparative statics, single crossing property JEL Classification: C60, C61, D i l , H21 Abstract This note provides sufficient conditions to draw Strict monotone comparative statics conclusions in optimization problems. These results extend the lattice-theoretic results of Milgrom and Shannon (1994) by imposing a stronger differential version of the single crossing property and arguing from first-order conditions. We illustrate the importance of these results through examples involving holdup problems and optimal tax problems. Thanks to Eric Emch, Steve Goldman, and Paul Milgrom for their comments. This work has been supported in part by the National Science Foundation under grant SBR-9321022.