The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Sangyeol Lee - One of the best experts on this subject based on the ideXlab platform.
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entropy test and residual Empirical Process for autoregressive conditional duration models
Computational Statistics & Data Analysis, 2015Co-Authors: Sangyeol LeeAbstract:In this paper, we study the entropy test for the goodness of fit test in (nonlinear) autoregressive conditional duration (ACD) models. To implement a test, we first explore the null limiting distribution of the residual Empirical Process from ACD models and verify that it has an asymptotic expansion form that consists of the true Empirical Process and extra terms yielded by parameter estimation. Then, we show that under regularity conditions, the proposed entropy test approximately follows a distribution that is free from the parameter estimation. For illustration, a simulation study and real data analysis are conducted. In the implementation of the test, a parametric bootstrap method is employed.
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Goodness of fit test for discrete random variables
Computational Statistics & Data Analysis, 2014Co-Authors: Sangyeol LeeAbstract:In this paper, a goodness of fit (gof) test for discrete random variables is studied. For the test, the Empirical Process gof test constructed based on the Khmaladze transformation method is considered to remove the parameter estimation effect. Further, the approach of the continuous extension of discrete random variables introduced in Denuit and Lambert (2005) is adopted. It is shown that under regularity conditions, the transformed Empirical Process weakly converges to a standard Brownian motion. As a gof test based on this result, the maximum entropy type test designed by Lee et al. (2011) is considered. As with the Empirical Process gof test, Vasicek's entropy test is also considered and a properly modified version, whose limiting distribution is unaffected by the choice of parameter estimates, is provided. Simulation results are provided for illustration.
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RESIDUAL Empirical Process FOR DIFFUSION ProcessES
Journal of the Korean Mathematical Society, 2008Co-Authors: Sangyeol Lee, In Suk WeeAbstract:In this paper, we study the asymptotic behavior of the residual Empirical Process from diffusion Processes. For this task, adopting the discrete sampling scheme as in Florens-Zmirou [9], we calculate the residuals and construct the residual Empirical Process. It is shown that the residual Empirical Process converges weakly to a Brownian bridge.
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Sequential Empirical Process in autoregressive models with measurement errors
Journal of Statistical Planning and Inference, 2006Co-Authors: Sangyeol Lee, Hyeonah ParkAbstract:In this paper, we study the weak convergence of the sequential Empirical Process based on the residuals from autoregressive models with measurement errors. It is shown that the sequential Empirical Process converges weakly to the sum of a Gaussian Process which is the limit of a sequential Empirical Process of certain p-dependent random variables and an additional term depending on the parameter estimators of the model. As an application, we discuss the change point problem in the distribution of the error Process in the autoregressive model. We present the numerical result of a simulation study for an asymptotically distribution-free test.
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A note on the residual Empirical Process in autoregressive models
Statistics & Probability Letters, 1997Co-Authors: Sangyeol LeeAbstract:Abstract Suppose that {Xt} is the stationary AR(p) Process of the form: Xt − μ = β1(Xt−1 − μ) + ⋯ + βp(Xt−p − μ) + et, where {et} is a sequence of i.i.d. random variables with mean zero and finite variance σ2. In this paper, we study the asymptotic behavior of the Empirical Process computed from the least-squares residuals, for which some estimators of μ and σ2 are substituted. Due to the estimation of the location and scale parameters, the limiting Process of the residual Empirical Process is shown to be a Gaussian Process which is not a standard Brownian bridge. The result is applicable to the goodness-of-fit test of the errors in autoregressive Processes.
David M Mason - One of the best experts on this subject based on the ideXlab platform.
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A uniform functional law of the logarithm for the local Empirical Process
The Annals of Probability, 2004Co-Authors: David M MasonAbstract:We prove a uniform functional law of the logarithm for the local Empirical Process. To accomplish this we combine techniques from classical and abstract Empirical Process theory, Gaussian distributional approximation and probability on Banach spaces. The body of techniques we develop should prove useful to the study of the strong consistency of d-variate kernel-type nonparametric function estimators.
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notes on the kmt brownian bridge approximation to the uniform Empirical Process
2001Co-Authors: David M MasonAbstract:Komlόs, Major, and Tusnady [KMT] (1975) published a Brownian bridge approximation to the uniform Empirical Process. However, the majority of the often very technical details of the proof were left to the reader. This has sometimes discouraged the acceptance and informed use of this very powerful approximation tool. The aim of these notes is to gain a wider audience for this beautiful result by making its proof more accessible. This is done by providing the details of the proof and pointing the reader to published work where they can be found.
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an Empirical Process approach to the uniform consistency of kernel type function estimators
Journal of Theoretical Probability, 2000Co-Authors: Uwe Einmahl, David M MasonAbstract:We use general Empirical Process methods to determine under mild regularity conditions exact rates of uniform strong consistency of kernel-type function estimators. In the Process a useful new bound on the expectation of the supremum of the Empirical Process is obtained
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asymptotic independence of the local Empirical Process indexed by functions
2000Co-Authors: Paul Deheuvels, Uwe Einmahl, David M MasonAbstract:We obtain independent joint strong approximations for multiple local Empirical Processes, which are independent of the approximation to the full Empirical Process. Applications include strong limit laws for iterated Empirical Processes.
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Gaussian approximation of local Empirical Processes indexed by functions
Probability Theory and Related Fields, 1997Co-Authors: Uwe Einmahl, David M MasonAbstract:An extended notion of a local Empirical Process indexed by functions is introduced, which includes kernel density and regression function estimators and the conditional Empirical Process as special cases. Under suitable regularity conditions a central limit theorem and a strong approximation by a sequence of Gaussian Processes are established for such Processes. A compact law of the iterated logarithm (LIL) is then inferred from the corresponding LIL for the approximating sequence of Gaussian Processes. A number of statistical applications of our results are indicated.
Emmanuel Rio - One of the best experts on this subject based on the ideXlab platform.
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Strong approximation results for the Empirical Process of stationary sequences
The Annals of Probability, 2013Co-Authors: Jérôme Dedecker, Florence Merlevède, Emmanuel RioAbstract:We prove a strong approximation result for the Empirical Process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also holds for the Empirical Process associated to iterates of expanding maps with a neutral fixed point at zero, as soon as the correlations decrease more rapidly than n−1−δ for some positive δ. This shows that our conditions are in some sense optimal.
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On strong approximation for the Empirical Process of stationary sequences
Annals of Probability, 2013Co-Authors: Jérôme Dedecker, Florence Merlevède, Emmanuel RioAbstract:We prove a strong approximation result for the Empirical Process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also holds for the Empirical Process associated to iterates of expanding maps with a neutral fixed point at zero, as soon as the correlations decrease more rapidly than n−(1+δ) for some positive δ. This shows that our conditions are in some sense optimal.
John H. J. Einmahl - One of the best experts on this subject based on the ideXlab platform.
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poisson and gaussian approximation of weighted local Empirical Processes
Stochastic Processes and their Applications, 1997Co-Authors: John H. J. EinmahlAbstract:We consider the local Empirical Process indexed by sets, a substantial generalization of the well-studied uniform tail Empirical Process. We show that the weak limit of weighted versions of this Process is Poisson under certain conditions, whereas it is Gaussian in other situations. Our main theorems provide many new results as well as a unified approach to a number of asymptotic distributional results for weighted Empirical Processes, which up to now appeared to be isolated facts. Our results have applications in ‘local’ statistical procedures; we will, in particular, show their usefulness in multivariate extreme value theory.
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poisson and gaussian approximation of weighted local Empirical Processes
Memorandum COSOR, 1995Co-Authors: John H. J. EinmahlAbstract:We consider the local Empirical Process indexed by sets, a greatly generalized version of the well-studied uniform tail Empirical Process. We show that the weak limit of weighted versions of this Process is Poisson under certain conditions, whereas it is Gaussian in other situations. Our main theorems provide a unified approach to a number of asymptotic distributional results for weighted Empirical Processes, which up to now appeared to be isolated facts. Our results are likely to have applications in local statistical procedures, e.g., in the study of multivariate extreme values.
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THE A.S. BEHAVIOR OF THE WEIGHTED Empirical Process AND THE LIL FOR THE WEIGHTED TAIL Empirical Process
The Annals of Probability, 1992Co-Authors: John H. J. EinmahlAbstract:The tail Empirical Process is defined to be for each n ? N, wn(t) = (n/kn)1/2an(tkn/n), 0 = t = 1, where an is the Empirical Process based on the first n of a sequence of independent uniform (0,1) random variables and {kn}8 n=1 is a sequence of positive numbers with kn/n ? 0 and kn ? 8. In this paper a complete description of the almost sure behavior of the weighted Empirical Process anan/q, where q is a weight function and {an}8 n=1 is a sequence of positive numbers, is established as well as a characterization of the law of the iterated logarithm behavior of the weighted tail Empirical Process wn/q, provided kn/loglog n ? 8. These results unify and generalize several results in the literature. Moreover, a characterization of the central limit theorem behavior of wn/q is presented. That result is applied to the construction of asymptotic confidence bands for intermediate quantiles from an arbitrary continuous distribution.
D. Hamadouche - One of the best experts on this subject based on the ideXlab platform.
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Weak convergence of smoothed Empirical Process in Hölder spaces
Statistics & Probability Letters, 1998Co-Authors: D. HamadoucheAbstract:Abstract The Brownian bridge is well known to have Holder continuous sample paths with exponent α 1 2 with probability one and to be the weak limit in C[0,1] of the smoothed Empirical Process based on the Empirical frequencies polygon. We propose to extend this weak convergence to Holder spaces. A general result for weak convergence in Holder spaces is proved. The weak convergence of the smoothed Empirical Process in each Holder space with exponent α 1 4 follows from this result. The bound α 1 4 is shown to be optimal. Convolution smoothing of the Empirical Process is also considered and leads to the bound α 1 2 .
