The study of the rodent fluctuations of the North was initiated in its modern form with Elton's pioneering work.Many scientific studies have been designed to collect yearly rodent abundance data,but the resulting ...The study of the rodent fluctuations of the North was initiated in its modern form with Elton's pioneering work.Many scientific studies have been designed to collect yearly rodent abundance data,but the resulting time series are generally subject to at least two "problems":being short and non-linear.We explore the use of the continuous threshold autoregressive(TAR) models for analyzing such data.In the simplest case,the continuous TAR models are additive autoregressive models,being piecewise linear in one lag,and linear in all other lags.The location of the slope change is called the threshold parameter.The continuous TAR models for rodent abundance data can be derived from a general prey-predator model under some simplifying assumptions.The lag in which the threshold is located sheds important insights on the structure of the prey-predator system.We propose to assess the uncertainty on the location of the threshold via a new bootstrap called the nearest block bootstrap(NBB) which combines the methods of moving block bootstrap and the nearest neighbor bootstrap.The NBB assumes an underlying finite-order time-homogeneous Markov process.Essentially,the NBB bootstraps blocks of random block sizes,with each block being drawn from a non-parametric estimate of the future distribution given the realized past bootstrap series.We illustrate the methods by simulations and on a particular rodent abundance time series from Kilpisjrvi,Northern Finland.展开更多
In this paper, we analyze the convergence of the adaptive conforming P 1 element method with the red-green refinement. Since the mesh after refining is not nested into the one before, the Galerkin-orthogonality does n...In this paper, we analyze the convergence of the adaptive conforming P 1 element method with the red-green refinement. Since the mesh after refining is not nested into the one before, the Galerkin-orthogonality does not hold for this case. To overcome such a difficulty, we prove some quasi-orthogonality instead under some mild condition on the initial mesh (Condition A). Consequently, we show convergence of the adaptive method by establishing the reduction of some total error. To weaken the condition on the initial mesh, we propose a modified red-green refinement and prove the convergence of the associated adaptive method under a much weaker condition on the initial mesh (Condition B).展开更多
Value at Risk (VaR) is a basic and very useful tool in measuring market risks. Numerous VaR models have been proposed in literature. Therefore, it is of great interest to evaluate the efficiency of these models, and t...Value at Risk (VaR) is a basic and very useful tool in measuring market risks. Numerous VaR models have been proposed in literature. Therefore, it is of great interest to evaluate the efficiency of these models, and to select the most appropriate one. In this paper, we shall propose to use the empirical likelihood approach to evaluate these models. Simulation results and real life examples show that the empirical likelihood method is more powerful and more robust than some of the asymptotic method available in literature.展开更多
This paper studies the least squares model averaging methods for two non-nested linear models.It is proved that the Mallows model averaging weight of the true model is root-n consistent.Then the authors develop a pena...This paper studies the least squares model averaging methods for two non-nested linear models.It is proved that the Mallows model averaging weight of the true model is root-n consistent.Then the authors develop a penalized Mallows criterion which ensures that the weight of the true model equals 1 with probability tending to 1 and thus the averaging estimator is asymptotically normal.If neither candidate model is true,the penalized Mallows averaging estimator is asymptotically optimal.Simulation results show the selection consistency of the penalized Mallows method and the superiority of the model averaging approach compared with the model selection estimation.展开更多
We present quantitative studies of transfer operators between finite element spaces associated with unrelated meshes.Several local approximations of the global L^(2)-orthogonal projection are reviewed and evaluated co...We present quantitative studies of transfer operators between finite element spaces associated with unrelated meshes.Several local approximations of the global L^(2)-orthogonal projection are reviewed and evaluated computationally.The numerical studies in 3D provide the first estimates of the quantitative differences between a range of transfer operators between non-nested finite element spaces.We consider the standard finite element interpolation,Cl´ement’s quasi-interpolation with different local polynomial degrees,the global L^(2)-orthogonal projection,a local L^(2)-quasi-projection via a discrete inner product,and a pseudo-L^(2)-projection defined by a Petrov-Galerkin variational equation with a discontinuous test space.Understanding their qualitative and quantitative behaviors in this computational way is interesting per se;it could also be relevant in the context of discretization and solution techniques which make use of different non-nested meshes.It turns out that the pseudo-L^(2)-projection approximates the actual L^(2)-orthogonal projection best.The obtained results seem to be largely independent of the underlying computational domain;this is demonstrated by four examples(ball,cylinder,half torus and Stanford Bunny).展开更多
This paper considers the post-J test inference in non-nested linear regression models. Post-J test inference means that the inference problem is considered by taking the first stage J test into account. We first propo...This paper considers the post-J test inference in non-nested linear regression models. Post-J test inference means that the inference problem is considered by taking the first stage J test into account. We first propose a post-J test estimator and derive its asymptotic distribution. We then consider the test problem of the unknown parameters, and a Wald statistic based on the post-J test estimator is proposed. A simulation study shows that the proposed Wald statistic works perfectly as well as the two-stage test from the view of the empirical size and power in large-sample cases, and when the sample size is small, it is even better. As a result,the new Wald statistic can be used directly to test the hypotheses on the unknown parameters in non-nested linear regression models.展开更多
基金supported by US National Science Foundation (Grant No. CMG-0620789)the Research GrantsCouncil of Hong Kong (Grant No. HKU7036/068)the Engineering and Physical Sciences Research Councilof UK (Grant No. EP/C549058/1)
文摘The study of the rodent fluctuations of the North was initiated in its modern form with Elton's pioneering work.Many scientific studies have been designed to collect yearly rodent abundance data,but the resulting time series are generally subject to at least two "problems":being short and non-linear.We explore the use of the continuous threshold autoregressive(TAR) models for analyzing such data.In the simplest case,the continuous TAR models are additive autoregressive models,being piecewise linear in one lag,and linear in all other lags.The location of the slope change is called the threshold parameter.The continuous TAR models for rodent abundance data can be derived from a general prey-predator model under some simplifying assumptions.The lag in which the threshold is located sheds important insights on the structure of the prey-predator system.We propose to assess the uncertainty on the location of the threshold via a new bootstrap called the nearest block bootstrap(NBB) which combines the methods of moving block bootstrap and the nearest neighbor bootstrap.The NBB assumes an underlying finite-order time-homogeneous Markov process.Essentially,the NBB bootstraps blocks of random block sizes,with each block being drawn from a non-parametric estimate of the future distribution given the realized past bootstrap series.We illustrate the methods by simulations and on a particular rodent abundance time series from Kilpisjrvi,Northern Finland.
基金supported by National Natural Science Foundation of China (Grant Nos.10601003, 10971005)Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No.200718) National Basic Research Program of China (Grant No. 2005CB321704)
文摘In this paper, we analyze the convergence of the adaptive conforming P 1 element method with the red-green refinement. Since the mesh after refining is not nested into the one before, the Galerkin-orthogonality does not hold for this case. To overcome such a difficulty, we prove some quasi-orthogonality instead under some mild condition on the initial mesh (Condition A). Consequently, we show convergence of the adaptive method by establishing the reduction of some total error. To weaken the condition on the initial mesh, we propose a modified red-green refinement and prove the convergence of the associated adaptive method under a much weaker condition on the initial mesh (Condition B).
基金supported by Guangdong Natural Science Foundation (Grant No.2008276)a grant from the Research Grants Council of Hong Kong,China
文摘Value at Risk (VaR) is a basic and very useful tool in measuring market risks. Numerous VaR models have been proposed in literature. Therefore, it is of great interest to evaluate the efficiency of these models, and to select the most appropriate one. In this paper, we shall propose to use the empirical likelihood approach to evaluate these models. Simulation results and real life examples show that the empirical likelihood method is more powerful and more robust than some of the asymptotic method available in literature.
基金supported by the National Natural Science Foundation of China under Grant Nos.11801598,12031016 and 11971323the National Statistical Research Program under Grant No.2018LY96+1 种基金the Beijing Natural Science Foundation under Grant No.1202001NQI Project under Grant No.2022YFF0609903.
文摘This paper studies the least squares model averaging methods for two non-nested linear models.It is proved that the Mallows model averaging weight of the true model is root-n consistent.Then the authors develop a penalized Mallows criterion which ensures that the weight of the true model equals 1 with probability tending to 1 and thus the averaging estimator is asymptotically normal.If neither candidate model is true,the penalized Mallows averaging estimator is asymptotically optimal.Simulation results show the selection consistency of the penalized Mallows method and the superiority of the model averaging approach compared with the model selection estimation.
基金supported by the Bonn International Graduate School in Mathematics and by the Iniziativa Ticino in Rete.
文摘We present quantitative studies of transfer operators between finite element spaces associated with unrelated meshes.Several local approximations of the global L^(2)-orthogonal projection are reviewed and evaluated computationally.The numerical studies in 3D provide the first estimates of the quantitative differences between a range of transfer operators between non-nested finite element spaces.We consider the standard finite element interpolation,Cl´ement’s quasi-interpolation with different local polynomial degrees,the global L^(2)-orthogonal projection,a local L^(2)-quasi-projection via a discrete inner product,and a pseudo-L^(2)-projection defined by a Petrov-Galerkin variational equation with a discontinuous test space.Understanding their qualitative and quantitative behaviors in this computational way is interesting per se;it could also be relevant in the context of discretization and solution techniques which make use of different non-nested meshes.It turns out that the pseudo-L^(2)-projection approximates the actual L^(2)-orthogonal projection best.The obtained results seem to be largely independent of the underlying computational domain;this is demonstrated by four examples(ball,cylinder,half torus and Stanford Bunny).
基金supported by a General Research Fund from the Hong Kong Research Grants Council(Grant No.City U-102709)National Natural Science Foundation of China(Grant Nos.11331011and 11271355)the Hundred Talents Program of the Chinese Academy of Sciences
文摘This paper considers the post-J test inference in non-nested linear regression models. Post-J test inference means that the inference problem is considered by taking the first stage J test into account. We first propose a post-J test estimator and derive its asymptotic distribution. We then consider the test problem of the unknown parameters, and a Wald statistic based on the post-J test estimator is proposed. A simulation study shows that the proposed Wald statistic works perfectly as well as the two-stage test from the view of the empirical size and power in large-sample cases, and when the sample size is small, it is even better. As a result,the new Wald statistic can be used directly to test the hypotheses on the unknown parameters in non-nested linear regression models.
