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Yixiao Sun - One of the best experts on this subject based on the ideXlab platform.
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let s fix it fixed b Asymptotics versus small b Asymptotics in heteroscedasticity and autocorrelation robust inference
Research Papers in Economics, 2013Co-Authors: Yixiao SunAbstract:In the presence of heteroscedasticity and autocorrelation of unknown forms, the covariance matrix of the parameter estimator is often estimated using a nonparametric kernel method that involves a lag truncation parameter. Depending on whether this lag truncation parameter is specified to grow at a slower rate than or the same rate as the sample size, we obtain two types of asymptotic approximations: the small-b Asymptotics and the fixed-b Asymptotics. Using techniques for probability distribution approximation and high order expansions, this paper shows that the fixed-b asymptotic approximation provides a higher order refinement to the first order small-b Asymptotics. This result provides a theoretical justification on the use of the fixed-b Asymptotics in empirical applications. On the basis of the fixed-b Asymptotics and higher order small-b Asymptotics, the paper introduces a new and easy-to-use asymptotic F test that employs a finite sample corrected Wald statistic and uses an F-distribution as the reference distribution. Finally, the paper develops a bandwidth selection rule that is testing-optimal in that the bandwidth minimizes the type II error of the asymptotic F test while controlling for its type I error. Monte Carlo simulations show that the asymptotic F test with the testing-optimal bandwidth works very well in finite samples.
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let s fix it fixed b Asymptotics versus small b Asymptotics in heteroscedasticity and autocorrelation robust inference
Social Science Research Network, 2010Co-Authors: Yixiao SunAbstract:In the presence of heteroscedasticity and autocorrelation of unknown forms, the covariance matrix of the parameter estimator is often estimated using a nonparametric kernel method that involves a lag truncation parameter. Depending on whether this lag truncation parameter is specified to grow at a slower rate than or the same rate as the sample size, we obtain two types of asymptotic approximations: the small-b Asymptotics and the fixed-b Asymptotics. Using techniques for probability distribution approximation and high order expansions, this paper shows that the fixed-b Asymptotics provides a higher order refinement to the first order small-b Asymptotics. This result provides a theoretical justification on the use of the fixed-b Asymptotics in empirical applications. On the basis of the fixed-b Asymptotics and higher order small-b Asymptotics, the paper introduces a new and easy-to-use F* test that employs a finite sample corrected Wald statistic and uses an F-distribution as the reference distribution. Finally, the paper develops a novel bandwidth selection rule that is testing-optimal in that the bandwidth minimizes the type II error of the F* test while controlling for its type I error. Monte Carlo simulations show that the F* test with the testing-optimal bandwidth works very well in finite samples.
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optimal bandwidth selection in heteroskedasticity autocorrelation robust testing
Social Science Research Network, 2006Co-Authors: Yixiao Sun, Peter C B Phillips, Sainan JinAbstract:In time series regressions with nonparametrically autocorrelated errors, it is now standard empirical practice to use kernel-based robust standard errors that involve some smoothing function over the sample autocorrelations. The underlying smoothing parameter b, which can be defined as the ratio of the bandwidth (or truncation lag) to the sample size, is a tuning parameter that plays a key role in determining the asymptotic properties of the standard errors and associated semi-parametric tests. Small-b Asymptotics involve standard limit theory such as standard normal or chi-squared limits, whereas fixed-b Asymptotics typically lead to nonstandard limit distributions involving Brownian bridge functionals. The present paper shows that the nonstandard fixed-b limit distributions of such nonparametrically studentized tests provide more accurate approximations to the finite sample distributions than the standard small-b limit distribution. In particular, using asymptotic expansions of both the finite sample distribution and the nonstandard limit distribution, we confirm that the second-order corrected critical value based on the expansion of the nonstandard limiting distribution is also second-order correct under the standard small-b Asymptotics. We further show that, for typical economic time series, the optimal bandwidth that minimizes a weighted average of type I and type II errors is larger by an order of magnitude than the bandwidth that minimizes the asymptotic mean squared error of the corresponding long-run variance estimator. A plug-in procedure for implementing this optimal bandwidth is suggested and simulations confirm that the new plug-in procedure works well in finite samples.
Jonathan S Chapman - One of the best experts on this subject based on the ideXlab platform.
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three dimensional capillary waves due to a submerged source with small surface tension
Journal of Fluid Mechanics, 2019Co-Authors: Christopher J Lustri, Ravindra Pethiyagoda, Jonathan S ChapmanAbstract:Steady and unsteady linearised flow past a submerged source are studied in the small-surface-tension limit, in the absence of gravitational effects. The free-surface capillary waves generated are exponentially small in the surface tension, and are determined using the theory of exponential Asymptotics. In the steady problem, capillary waves are found to extend upstream from the source, switching on across curves on the free surface known as Stokes lines. Asymptotic predictions are compared with computational solutions for the position of the free surface. In the unsteady problem, transient effects cause the solution to display more complicated asymptotic behaviour, such as higher-order Stokes lines. The theory of exponential Asymptotics is applied to show how the capillary waves evolve over time, and eventually tend to the steady solution.
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three dimensional capillary waves due to a submerged source with small surface tension
arXiv: Fluid Dynamics, 2018Co-Authors: Christopher J Lustri, Ravindra Pethiyagoda, Jonathan S ChapmanAbstract:Steady and unsteady linearised flow past a submerged source are studied in the small-surface-tension limit, in the absence of gravitational effects. The free-surface capillary waves generated are exponentially small in the surface tension, and are determined using the theory of exponential Asymptotics. In the steady problem, capillary waves are found to extend upstream from the source, switching on across curves on the free surface known as Stokes lines. Asymptotic predictions and compared with computational solutions for the position of the free surface. In the unsteady problem, transient effects cause the solution to display more complicated asymptotic behaviour, such as higher-order Stokes lines. The theory of exponential Asymptotics is applied to show how the capillary waves evolve over time, and eventually tend to the steady solution.
Kenneth Tr D Mclaughlin - One of the best experts on this subject based on the ideXlab platform.
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Asymptotics for the partition function in two cut random matrix models
Communications in Mathematical Physics, 2015Co-Authors: Tom Claeys, Tamara Grava, Kenneth Tr D MclaughlinAbstract:We obtain large N Asymptotics for the random matrix partition function $$Z_N(V)=\int_{\mathbb{R}^N} \prod_{i < j}(x_i-x_j)^2\prod_{j=1}^Ne^{-NV(x_j)}dx_j,$$ in the case where V is a polynomial such that the random matrix eigenvalues accumulate on two disjoint intervals (the two-cut case). We compute leading and sub-leading terms in the asymptotic expansion for log ZN(V), up to terms that are small as \({N \to \infty}\). Our approach is based on the explicit computation of the first terms in the asymptotic expansion for a quartic symmetric potential V. Afterwards, we use deformation theory of the partition function and of the associated equilibrium measure to generalize our results to general two-cut potentials V. The asymptotic expansion of log ZN(V) as \({N \to \infty}\) contains terms that depend analytically on the potential V and that have already appeared in the literature. In addition, our method allows us to compute the V-independent terms of the asymptotic expansion of log ZN(V) which, to the best of our knowledge, had not appeared before in the literature. We use rigorous orthogonal polynomial and Riemann–Hilbert techniques, which had to this point only been successful to compute Asymptotics for the partition function in the one-cut case.
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Asymptotics for the partition function in two cut random matrix models
arXiv: Mathematical Physics, 2014Co-Authors: Tom Claeys, Tamara Grava, Kenneth Tr D MclaughlinAbstract:We obtain large N Asymptotics for the Hermitian random matrix partition function \[Z_N(V)=\int_{\mathbb R^N}\prod_{i
Hans Lindblad - One of the best experts on this subject based on the ideXlab platform.
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asymptotic behavior of the maxwell klein gordon system
Communications in Mathematical Physics, 2019Co-Authors: Timothy Candy, Christopher Kauffman, Hans LindbladAbstract:In previous work on the Maxwell–Klein–Gordon system, first global existence and then decay estimates have been shown. Here we show that the Maxwell–Klein–Gordon system in the Lorenz gauge satisfies the weak null condition and give detailed Asymptotics for the scalar field and the potential. These Asymptotics have two parts, one wave like along outgoing light cones at null infinity, and one homogeneous inside the light cone at time like infinity. Here, the charge plays a crucial role in imposing an oscillating factor in the asymptotic system for the field, and in the null Asymptotics for the potential. The Maxwell–Klein–Gordon system, apart from being of interest in its own right, also provides a simpler semi-linear model of the quasi-linear Einstein’s equations where similar asymptotic results have previously been obtained in wave coordinates.
N N Nefedov - One of the best experts on this subject based on the ideXlab platform.
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existence and stability of periodic contrast structures in the reaction advection diffusion problem
Russian Journal of Mathematical Physics, 2015Co-Authors: N N Nefedov, E I NikulinAbstract:A singularly perturbed periodic problem for a parabolic reaction-advection-diffusion equation at low advection is studied. The case when there is an internal transition layer under unbalanced nonlinearity is considered. An asymptotic expansion of a solution is constructed. To substantiate the Asymptotics thus constructed, the asymptotic method of differential inequalities is used. The Lyapunov asymptotic stability of a periodic solution is studied; the proof uses the Krein-Rutman theorem.
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Asymptotics of the front motion in the reaction diffusion advection problem
Computational Mathematics and Mathematical Physics, 2014Co-Authors: E A Antipov, N T Levashova, N N NefedovAbstract:A singularly perturbed initial boundary value problem is considered for a parabolic equation that is known in application as the reaction-diffusion-advection equation. An asymptotic expansion of solutions with a moving front is constructed. This Asymptotics is proved by the method of differential inequalities, which is based on well-known comparison theorems and develops the ideas of formal Asymptotics for constructing upper and lower solutions in singularly perturbed problems with internal and boundary layers.
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existence and asymptotic stability of periodic solutions with an interior layer of reaction advection diffusion equations
Journal of Mathematical Analysis and Applications, 2013Co-Authors: N N Nefedov, Lutz Recke, K R SchneiderAbstract:Abstract We consider a singularly perturbed parabolic periodic boundary value problem for a reaction–advection–diffusion equation. We construct the interior layer type formal Asymptotics and propose a modified procedure to get asymptotic lower and upper solutions. By using sufficiently precise lower and upper solutions, we prove the existence of a periodic solution with an interior layer and estimate the accuracy of its Asymptotics. Moreover, we are able to establish the asymptotic stability of this solution.
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front motion in the parabolic reaction diffusion problem
Computational Mathematics and Mathematical Physics, 2010Co-Authors: Yu V Bozhevolnov, N N NefedovAbstract:A singularly perturbed initial-boundary value problem is considered for a parabolic equation known in applications as the reaction-diffusion equation. An asymptotic expansion of solutions with a moving front is constructed, and an existence theorem for such solutions is proved. The asymptotic expansion is substantiated using the asymptotic method of differential inequalities, which is extended to the class of problems under study. The method is based on well-known comparison theorems and is a development of the idea of using formal Asymptotics for the construction of upper and lower solutions in singularly perturbed problems with internal and boundary layers.
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the cauchy problem for a singularly perturbed integro differential fredholm equation
Computational Mathematics and Mathematical Physics, 2007Co-Authors: N N Nefedov, A G NikitinAbstract:An initial problem is considered for an ordinary singularly perturbed integro-differential equation with a nonlinear integral Fredholm operator. The case when the reduced equation has a smooth solution is investigated, and the solution to the reduced equation with a corner point is analyzed. The Asymptotics of the solution to the Cauchy problem is constructed by the method of boundary functions. The Asymptotics is validated by the asymptotic method of differential inequalities developed for a new class of problems.
