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William H Greene - One of the best experts on this subject based on the ideXlab platform.
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fixed effects vector decomposition a magical solution to the problem of time invariant variables in fixed effects models
Political Analysis, 2011Co-Authors: William H GreeneAbstract:In “Efficient Estimation of Time Invariant and Rarely Changing Variables in Finite Sample Panel Analyses with Unit Fixed Effects,” Plumper and Troeger (2007), propose a three step procedure for the estimation of fixed effects models that, it is claimed, “provides the most reliable estimates under a wide variety of specifications common to real world data.” Their FEVD estimator is startlingly simple, involving three trivial steps, each requiring nothing more than ordinary least squares. Large gains in efficiency are claimed for cases of time invariant and slowly time varying regressors. A subsequent literature has compared the estimator to other estimators of fixed effects models, including Hausman and Taylor’s (1981) estimator, also (apparently) with impressive gains in efficiency. The article also claims to provide an efficient estimator for parameters on time invariant variables in the fixed effects model. None of the claims are correct. The FEVD estimator simply reproduces (identically) the linear fixed effects (dummy variable) estimator then substitutes an inappropriate covariance matrix for the correct one. The Consistency Result follows from the fact that OLS in the FE model is consistent. The “efficiency” gains are illusory. The claim that the estimator provides an estimator for the coefficients on time invariant variables in a fixed effects model is also incorrect. That part of the parameter vector remains unidentified. The “estimator” relies upon turning the fixed effects model into a random effects model, in which case simple GLS estimation of all (now identified) parameters would be efficient among all estimators.
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fixed effects vector decomposition a magical solution to the problem of time invariant variables in fixed effects models
Political Analysis, 2011Co-Authors: William H GreeneAbstract:Plumper and Troeger (2007) propose a three-step procedure for the estimation of a fixed effects (FE) model that, it is claimed, “provides the most reliable estimates under a wide variety of specifications common to real world data.” Their fixed effects vector decomposition (FEVD) estimator is startlingly simple, involving three simple steps, each requiring nothing more than ordinary least squares (OLS). Large gains in efficiency are claimed for cases of time-invariant and slowly time-varying regressors. A subsequent literature has compared the estimator to other estimators of FE models, including the estimator of Hausman and Taylor (1981) also (apparently) with impressive gains in efficiency. The article also claims to provide an efficient estimator for parameters on time-invariant variables (TIVs) in the FE model. None of the claims are correct. The FEVD estimator simply reproduces (identically) the linear FE (dummy variable) estimator then substitutes an inappropriate covariance matrix for the correct one. The Consistency Result follows from the fact that OLS in the FE model is consistent. The “efficiency” gains are illusory. The claim that the estimator provides an estimator for the coefficients on TIVs in an FE model is also incorrect. That part of the parameter vector remains unidentified. The “estimator” relies upon a strong assumption that turns the FE model into a type of random effects model.
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fixed effects vector decomposition a magical solution to the problem of time invariant variables in fixed effects models
2010Co-Authors: William H GreeneAbstract:PlA¼mper and Troeger (2007) propose a three-step procedure for the estimation of a fixed effects (FE) model that, it is claimed, “provides the most reliable estimates under a wide variety of specifications common to real world data.†Their fixed effects vector decomposition (FEVD) estimator is startlingly simple, involving three simple steps, each requiring nothing more than ordinary least squares (OLS). Large gains in efficiency are claimed for cases of time-invariant and slowly time-varying regressors. A subsequent literature has compared the estimator to other estimators of FE models, including the estimator of Hausman and Taylor (1981) also (apparently) with impressive gains in efficiency. The article also claims to provide an efficient estimator for parameters on time-invariant variables (TIVs) in the FE model. None of the claims are correct. The FEVD estimator simply reproduces (identically) the linear FE (dummy variable) estimator then substitutes an inappropriate covariance matrix for the correct one. The Consistency Result follows from the fact that OLS in the FE model is consistent. The “efficiency†gains are illusory. The claim that the estimator provides an estimator for the coefficients on TIVs in an FE model is also incorrect. That part of the parameter vector remains unidentified. The “estimator†relies upon a strong assumption that turns the FE model into a type of random effects model. (This abstract was borrowed from another version of this item.)
Juan Carlos Martinez - One of the best experts on this subject based on the ideXlab platform.
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a Consistency Result on long cardinal sequences
Annals of Pure and Applied Logic, 2021Co-Authors: Juan Carlos Martinez, Lajos SoukupAbstract:Abstract For any regular cardinal κ and ordinal η κ + + it is consistent that 2 κ is as large as you wish, and every function f : η ⟶ [ κ , 2 κ ] ∩ C a r d with f ( α ) = κ for c f ( α ) κ is the cardinal sequence of some locally compact scattered space.
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a Consistency Result on long cardinal sequences
arXiv: Logic, 2019Co-Authors: Juan Carlos Martinez, Lajos SoukupAbstract:For any regular cardinal $\kappa$ and ordinal $\eta<\kappa^{++}$ it is consistent that $2^{\kappa}$ is as large as you wish, and every function $f:\eta \to [\kappa,2^{\kappa}]\cap Card$ with $f(\alpha)=\kappa$ for $cf(\alpha)<\kappa$ is the cardinal sequence of some locally compact scattered space.
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superatomic boolean algebras constructed from strongly unbounded functions
Mathematical Logic Quarterly, 2011Co-Authors: Juan Carlos Martinez, Lajos SoukupAbstract:Using Koszmider's strongly unbounded functions, we show the following Consistency Result: Suppose that κ, λ are infinite cardinals such that κ++ + ≤ λ, κ<κ = κ and 2κ = κ+, and η is an ordinal with κ+ ≤ η < κ++ and cf(η) = κ+. Then, in some cardinal-preserving generic extension there is a superatomic Boolean algebra such that , for every α < η and (i.e., there is a locally compact scattered space with cardinal sequence 〈κ〉η⌢〈λ〉). Especially, and can be cardinal sequences of superatomic Boolean algebras.
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superatomic boolean algebras constructed from strongly unbounded functions
arXiv: Logic, 2010Co-Authors: Juan Carlos Martinez, Lajos SoukupAbstract:Using Koszmider's strongly unbounded functions, we show the following Consistency Result: Suppose that $\kappa,\lambda$ are infinite cardinals such that $\kappa^{+++} \leq \lambda$, $\kappa^{<\kappa}=\kappa$ and $2^{\kappa}= \kappa^+$, and $\eta$ is an ordinal with $\kappa^+\leq \eta <\kappa^{++}$ and $cf(\eta) = \kappa^+$. Then, in some cardinal-preserving generic extension there is a superatomic Boolean algebra $B$ such that - $ht(B) = \eta + 1$, - the cardinality of the $\alpha$th level of $B$ is $\kappa$ for every $\alpha _{{\omega}_1}\concatenation \ $ and $\ _{{\omega}_2}\concatenation \ $ can be cardinal sequences of superatomic Boolean algebras.
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a Consistency Result on cardinal sequences of scattered boolean spaces
Mathematical Logic Quarterly, 2005Co-Authors: Juan Carlos MartinezAbstract:We prove that if GCH holds and τ = 〈κα : α < η 〉 is a sequence of infinite cardinals such that κα ≥ |η | for each α < η, then there is a cardinal-preserving partial order that forces the existence of a scattered Boolean space whose cardinal sequence is τ. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Lan Wang - One of the best experts on this subject based on the ideXlab platform.
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a consistent information criterion for support vector machines in diverging model spaces
Journal of Machine Learning Research, 2016Co-Authors: Xiang Zhang, Lan WangAbstract:Information criteria have been popularly used in model selection and proved to possess nice theoretical properties. For classification, Claeskens et al. (2008) proposed support vector machine information criterion for feature selection and provided encouraging numerical evidence. Yet no theoretical justification was given there. This work aims to fill the gap and to provide some theoretical justifications for support vector machine information criterion in both fixed and diverging model spaces. We first derive a uniform convergence rate for the support vector machine solution and then show that a modification of the support vector machine information criterion achieves model selection Consistency even when the number of features diverges at an exponential rate of the sample size. This Consistency Result can be further applied to selecting the optimal tuning parameter for various penalized support vector machine methods. Finite-sample performance of the proposed information criterion is investigated using Monte Carlo studies and one real-world gene selection problem.
Lajos Soukup - One of the best experts on this subject based on the ideXlab platform.
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a Consistency Result on long cardinal sequences
Annals of Pure and Applied Logic, 2021Co-Authors: Juan Carlos Martinez, Lajos SoukupAbstract:Abstract For any regular cardinal κ and ordinal η κ + + it is consistent that 2 κ is as large as you wish, and every function f : η ⟶ [ κ , 2 κ ] ∩ C a r d with f ( α ) = κ for c f ( α ) κ is the cardinal sequence of some locally compact scattered space.
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a Consistency Result on long cardinal sequences
arXiv: Logic, 2019Co-Authors: Juan Carlos Martinez, Lajos SoukupAbstract:For any regular cardinal $\kappa$ and ordinal $\eta<\kappa^{++}$ it is consistent that $2^{\kappa}$ is as large as you wish, and every function $f:\eta \to [\kappa,2^{\kappa}]\cap Card$ with $f(\alpha)=\kappa$ for $cf(\alpha)<\kappa$ is the cardinal sequence of some locally compact scattered space.
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superatomic boolean algebras constructed from strongly unbounded functions
Mathematical Logic Quarterly, 2011Co-Authors: Juan Carlos Martinez, Lajos SoukupAbstract:Using Koszmider's strongly unbounded functions, we show the following Consistency Result: Suppose that κ, λ are infinite cardinals such that κ++ + ≤ λ, κ<κ = κ and 2κ = κ+, and η is an ordinal with κ+ ≤ η < κ++ and cf(η) = κ+. Then, in some cardinal-preserving generic extension there is a superatomic Boolean algebra such that , for every α < η and (i.e., there is a locally compact scattered space with cardinal sequence 〈κ〉η⌢〈λ〉). Especially, and can be cardinal sequences of superatomic Boolean algebras.
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superatomic boolean algebras constructed from strongly unbounded functions
arXiv: Logic, 2010Co-Authors: Juan Carlos Martinez, Lajos SoukupAbstract:Using Koszmider's strongly unbounded functions, we show the following Consistency Result: Suppose that $\kappa,\lambda$ are infinite cardinals such that $\kappa^{+++} \leq \lambda$, $\kappa^{<\kappa}=\kappa$ and $2^{\kappa}= \kappa^+$, and $\eta$ is an ordinal with $\kappa^+\leq \eta <\kappa^{++}$ and $cf(\eta) = \kappa^+$. Then, in some cardinal-preserving generic extension there is a superatomic Boolean algebra $B$ such that - $ht(B) = \eta + 1$, - the cardinality of the $\alpha$th level of $B$ is $\kappa$ for every $\alpha _{{\omega}_1}\concatenation \ $ and $\ _{{\omega}_2}\concatenation \ $ can be cardinal sequences of superatomic Boolean algebras.
Yutang Shi - One of the best experts on this subject based on the ideXlab platform.
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estimation and inference of change points in high dimensional factor models
Journal of Econometrics, 2020Co-Authors: Jushan Bai, Xu Han, Yutang ShiAbstract:Abstract In this paper, we consider the estimation of break points in high-dimensional factor models where the unobserved factors are estimated by principal component analysis (PCA). The factor loading matrix is assumed to have a structural break at an unknown time. We establish the conditions under which the least squares (LS) estimator is consistent for the break date. Our Consistency Result holds for both large and small breaks. We also find the LS estimator’s asymptotic distribution. Simulation Results confirm that the break date can be accurately estimated by the LS even if the magnitudes of breaks are small. In two empirical applications, we implement the method to estimate break points in the U.S. stock market and U.S. macroeconomy, respectively.
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estimation and inference of change points in high dimensional factor models
Social Science Research Network, 2018Co-Authors: Jushan Bai, Xu Han, Yutang ShiAbstract:This paper considers the estimation of break point in high dimensional factor models where the unobserved factors are estimated by Principal Component Analysis (PCA). The factor loading matrix is assumed to have a structural break at a certain time. We establish the conditions under which the least squares (LS) estimator is consistent for the break date. Our Consistency Result holds for smaller breaks than those in the existing literature. We also find the LS estimator’s asymptotic distribution, which depends on the data generating process of the unobserved factors. Simulation Results confirm that the break date can be accurately estimated by the LS even if the breaks are small. In two empirical applications, we implement our method to estimate the break points in the U.S. stock market and U.S. macroeconomy, respectively.