The Experts below are selected from a list of 111939 Experts worldwide ranked by ideXlab platform
Halbert White - One of the best experts on this subject based on the ideXlab platform.
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Asymptotic Distribution theory for nonparametric entropy measures of serial dependence
2005Co-Authors: Yongmiao Hong, Halbert WhiteAbstract:Entropy is a classical statistical concept with appealing properties. Establishing Asymptotic Distribution theory for smoothed nonparametric entropy measures of dependence has so far proved challenging. In this paper, we develop an Asymptotic theory for a class of kernel-based smoothed nonparametric entropy measures of serial dependence in a time-series context. We use this theory to derive the limiting Distribution of Granger and Lin's (1994) normalized entropy measure of serial dependence, which was previously not available in the literature. We also apply our theory to construct a new entropy-based test for serial dependence, providing an alternative to Robinson's (1991) approach. To obtain accurate inferences, we propose and justify a consistent smoothed bootstrap procedure. The naive bootstrap is not consistent for our test. Our test is useful in, for example, testing the random walk hypothesis, evaluating density forecasts, and identifying important lags of a time series. It is Asymptotically locally more powerful than Robinson's (1991) test, as is confirmed in our simulation. An application to the daily S&P 500 stock price index illustrates our approach. Copyright The Econometric Society 2005.
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Asymptotic Distribution THEORY FOR NONPARAMETRIC ENTROPY MEASURES OF SERIAL DEPENDENCE
2005Co-Authors: Yongmiao Hong, Halbert WhiteAbstract:Entropy is a classical statistical concept with appealing properties. Establishing Asymptotic Distribution theory for smoothed nonparametric entropy measures of dependence has so far proved challenging. In this paper, we develop an Asymptotic theory for a class of kernel-based smoothed nonparametric entropy measures of serial dependence in a time-series context. We use this theory to derive the limiting Distribution of Granger and Lin's (1994) normalized entropy measure of serial dependence, which was previously not available in the literature. We also apply our theory to construct a new entropy-based test for serial dependence, providing an alternative to Robinson's (1991) approach. To obtain accurate inferences, we propose and justify a consistent smoothed bootstrap procedure. The naive bootstrap is not consistent for our test. Our test is useful in, for example, testing the random walk hypothesis, evaluating density forecasts, and identifying important lags of a time series. It is Asymptotically locally more powerful than Robinson's (1991) test, as is confirmed in our simulation. An application to the daily S&P 500 stock price index illustrates our approach.
Peter M Visscher - One of the best experts on this subject based on the ideXlab platform.
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a note on the Asymptotic Distribution of likelihood ratio tests to test variance components
2006Co-Authors: Peter M VisscherAbstract:When using maximum likelihood methods to estimate genetic and environmental components of (co)variance, it is common to test hypotheses using likelihood ratio tests, since such tests have desirable Asymptotic properties. In particular, the standard likelihood ratio test statistic is assumed Asymptotically to follow a chi(2) Distribution with degrees of freedom equal to the number of parameters tested. Using the relationship between least squares and maximum likelihood estimators for balanced designs, it is shown why the Asymptotic Distribution of the likelihood ratio test for variance components does not follow a chi(2) Distribution with degrees of freedom equal to the number of parameters tested when the null hypothesis is true. Instead, the Distribution of the likelihood ratio test is a mixture of chi(2) Distributions with different degrees of freedom. Implications for testing variance components in twin designs and for quantitative trait loci mapping are discussed. The appropriate Distribution of the likelihood ratio test statistic should be used in hypothesis testing and model selection.
Kui Zhang - One of the best experts on this subject based on the ideXlab platform.
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fluid heterogeneity detection based on the Asymptotic Distribution of the time averaged mean squared displacement in single particle tracking experiments
2018Co-Authors: Kui Zhang, Katelyn P R Crizer, Mark H Schoenfisch, David B Hill, Gustavo DidierAbstract:: A tracer particle is called anomalously diffusive if its mean squared displacement grows approximately as σ2tα as a function of time t for some constant σ2, where the diffusion exponent satisfies α ≠ 1. In this article, we use recent results on the Asymptotic Distribution of the time-averaged mean squared displacement [20] to construct statistical tests for detecting physical heterogeneity in viscoelastic fluid samples starting from one or multiple observed anomalously diffusive paths. The methods are Asymptotically valid for the range 0 < α < 3/2 and involve a mathematical characterization of time-averaged mean squared displacement bias and the effect of correlated disturbance errors. The assumptions on particle motion cover a broad family of fractional Gaussian processes, including fractional Brownian motion and many fractional instances of the generalized Langevin equation framework. We apply the proposed methods in experimental data from treated P. aeruginosa biofilms generated by the collaboration of the Hill and Schoenfisch Labs at UNC-Chapel Hill.
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fluid heterogeneity detection based on the Asymptotic Distribution of the time averaged mean squared displacement in single particle tracking experiments
2018Co-Authors: Kui Zhang, Katelyn P R Crizer, Mark H Schoenfisch, David B Hill, Gustavo DidierAbstract:A tracer particle is called anomalously diffusive if its mean squared displacement grows approximately as $\sigma^2 t^{\alpha}$ as a function of time $t$ for some constant $\sigma^2$, where the diffusion exponent satisfies $\alpha \neq 1$. In this article, we use recent results on the Asymptotic Distribution of the time-averaged mean squared displacement (Didier and Zhang (2017)) to construct statistical tests for detecting physical heterogeneity in viscoelastic fluid samples starting from one or multiple observed anomalously diffusive paths. The methods are Asymptotically valid for the range $0 < \alpha < 3/2$ and involve a mathematical characterization of time-averaged mean squared displacement bias and the effect of correlated disturbance errors. The assumptions on particle motion cover a broad family of fractional Gaussian processes, including fractional Brownian motion and many fractional instances of the generalized Langevin equation framework. We apply the proposed methods in experimental data from treated $P.\ aeruginosa$ biofilms generated by the collaboration of the Hill and Schoenfisch Labs at UNC-Chapel Hill.
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the Asymptotic Distribution of the pathwise mean squared displacement in single particle tracking experiments
2017Co-Authors: Gustavo Didier, Kui ZhangAbstract:Microrheology is the study of the properties of biological complex fluids through the anomalous diffusion of small embedded particles. The main statistic for characterizing anomalous diffusion is the so-named mean squared displacement (MSD) of the particles. Notwithstanding the central statistical role of the MSD, its Asymptotic Distribution has not yet been established. In this paper, we assume that the particle motion is a Gaussian, stationary-increment stochastic process. We show that as the sample and the increment lag sizes go to infinity, the MSD displays Gaussian or non-Gaussian limiting Distributions, as well as distinct convergence rates, depending on the diffusion exponent parameter.
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the Asymptotic Distribution of the pathwise mean squared displacement in single particle tracking experiments
2015Co-Authors: Gustavo Didier, Kui ZhangAbstract:Recent advances in light microscopy have spawned new research frontiers in microbiology by working around the diffraction barrier and allowing for the observation of nanometric biological structures. Microrheology is the study of the properties of complex fluids, such as those found in biology, through the dynamics of small embedded particles, typically latex beads. Statistics based on the recorded sample paths are then used by biophysicists to infer rheological properties of the fluid. In the biophysical literature, the main statistic for characterizing diffusivity is the so-named mean square displacement (MSD) of the tracer particles. Notwithstanding the central role played by the MSD, its Asymptotic Distribution in different cases has not yet been established. In this paper, we tackle this problem. We take a pathwise approach and assume that the particle movement undergoes a Gaussian, stationary-increment stochastic process. We show that as the sample and the increment lag sizes go to infinity, the MSD displays Gaussian or non-Gaussian limiting Distributions, as well as distinct convergence rates, depending on the diffusivity parameter. We illustrate our results analytically and computationally based on fractional Brownian motion and the (integrated) fractional Ornstein-Uhlenbeck process.
Francois Longin - One of the best experts on this subject based on the ideXlab platform.
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the Asymptotic Distribution of extreme stock market returns
2000Co-Authors: Francois LonginAbstract:This article presents a study of extreme stock market price movements. According to extreme value theory, the form of the Distribution of extreme returns is precisely known and independent of the process generating returns. Using data for an index of the most traded stocks on the New York Stock Exchange for the period 1885-1990, it is shown empirically that the extreme returns obey a Frechet Distribution.
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the Asymptotic Distribution of extreme stock market returns
1996Co-Authors: Francois LonginAbstract:This article presents a study of extreme stock market price movements. According to extreme value theory, the form of the Distribution of extreme returns is precisely known and independent of the process generating returns. Using data for an index of the most traded stocks on the New York Stock Exchange for the period 1885-1990, the author shows empirically that the extreme returns obey a Frechet Distribution. Copyright 1996 by University of Chicago Press.
Yongmiao Hong - One of the best experts on this subject based on the ideXlab platform.
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Asymptotic Distribution theory for nonparametric entropy measures of serial dependence
2005Co-Authors: Yongmiao Hong, Halbert WhiteAbstract:Entropy is a classical statistical concept with appealing properties. Establishing Asymptotic Distribution theory for smoothed nonparametric entropy measures of dependence has so far proved challenging. In this paper, we develop an Asymptotic theory for a class of kernel-based smoothed nonparametric entropy measures of serial dependence in a time-series context. We use this theory to derive the limiting Distribution of Granger and Lin's (1994) normalized entropy measure of serial dependence, which was previously not available in the literature. We also apply our theory to construct a new entropy-based test for serial dependence, providing an alternative to Robinson's (1991) approach. To obtain accurate inferences, we propose and justify a consistent smoothed bootstrap procedure. The naive bootstrap is not consistent for our test. Our test is useful in, for example, testing the random walk hypothesis, evaluating density forecasts, and identifying important lags of a time series. It is Asymptotically locally more powerful than Robinson's (1991) test, as is confirmed in our simulation. An application to the daily S&P 500 stock price index illustrates our approach. Copyright The Econometric Society 2005.
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Asymptotic Distribution THEORY FOR NONPARAMETRIC ENTROPY MEASURES OF SERIAL DEPENDENCE
2005Co-Authors: Yongmiao Hong, Halbert WhiteAbstract:Entropy is a classical statistical concept with appealing properties. Establishing Asymptotic Distribution theory for smoothed nonparametric entropy measures of dependence has so far proved challenging. In this paper, we develop an Asymptotic theory for a class of kernel-based smoothed nonparametric entropy measures of serial dependence in a time-series context. We use this theory to derive the limiting Distribution of Granger and Lin's (1994) normalized entropy measure of serial dependence, which was previously not available in the literature. We also apply our theory to construct a new entropy-based test for serial dependence, providing an alternative to Robinson's (1991) approach. To obtain accurate inferences, we propose and justify a consistent smoothed bootstrap procedure. The naive bootstrap is not consistent for our test. Our test is useful in, for example, testing the random walk hypothesis, evaluating density forecasts, and identifying important lags of a time series. It is Asymptotically locally more powerful than Robinson's (1991) test, as is confirmed in our simulation. An application to the daily S&P 500 stock price index illustrates our approach.
