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Yongmiao Hong - One of the best experts on this subject based on the ideXlab platform.

  • Testing for pairwise serial independence via the Empirical Distribution Function
    Journal of the Royal Statistical Society: Series B (Statistical Methodology), 1998
    Co-Authors: Yongmiao Hong
    Abstract:

    Built on Skaug and Tjostheim's approach, this paper proposes a new test for serial independence by comparing the pairwise Empirical Distribution Functions of a time series with the products of its marginals for various lags, where the number of lags increases with the sample size and different lags are assigned different weights. Typically, the more recent information receives a larger weight. The test has some appealing attributes. It is consistent against all pairwise dependences and is powerful against alternatives whose dependence decays to zero as the lag increases. Although the test statistic is a weighted sum of degenerate Cramer–von Mises statistics, it has a null asymptotic N(0, 1) Distribution. The test statistic and its limit Distribution are invariant to any order preserving transformation. The test applies to time series whose Distributions can be discrete or continuous, with possibly infinite moments. Finally, the test statistic only involves ranking the observations and is computationally simple. It has the advantage of avoiding smoothed nonparametric estimation. A simulation experiment is conducted to study the finite sample performance of the proposed test in comparison with some related tests.

  • Testing for pairwise serial independence via the Empirical Distribution Function Series B Statistical methodology
    Journal of the Royal Statistical Society, 1998
    Co-Authors: Yongmiao Hong
    Abstract:

    Built on Skaug and Tjostheim's approach, this paper proposes a new test for serial independence by comparing the pairwise Empirical Distribution Functions of a time series with the products of its marginals for various lags, where the number of lags increases with the sample size and different lags are assigned different weights. Typically, the more recent information receives a larger weight. The test has some appealing attributes. It is consistent against all pairwise dependences and is powerful against alternatives whose dependence decays to zero as the lag increases. Although the test statistic is a weighted sum of degenerate Cramer–von Mises statistics, it has a null asymptotic N(0, 1) Distribution. The test statistic and its limit Distribution are invariant to any order preserving transformation. The test applies to time series whose Distributions can be discrete or continuous, with possibly infinite moments. Finally, the test statistic only involves ranking the observations and is computationally simple. It has the advantage of avoiding smoothed nonparametric estimation. A simulation experiment is conducted to study the finite sample performance of the proposed test in comparison with some related tests.

Jushan Bai - One of the best experts on this subject based on the ideXlab platform.

  • Testing for Parameter Constancy in Linear Regressions: An Empirical Distribution Function Approach
    Econometrica, 1996
    Co-Authors: Jushan Bai
    Abstract:

    This paper proposes some tests for parameter constancy in linear regressions. The tests use weighted Empirical Distribution Functions of estimated residuals and are asymptotically Distribution free. The proposed tests have nontrivial local power against a wide range of alternatives. In particular, the tests are capable of detecting error heterogeneity that is not necessarily manifested in the form of changing variances. The model allows for both dynamic and trending regressors. As an intermediate result, some weak convergence for (stochastically) weighted sequential Empirical processes is established. Copyright 1996 by The Econometric Society.

Jérôme Dedecker - One of the best experts on this subject based on the ideXlab platform.

  • weak convergence of the Empirical process of intermittent maps in x1d543 2 under long range dependence
    Stochastics and Dynamics, 2015
    Co-Authors: Jérôme Dedecker, Herold Dehling, Murad S Taqqu
    Abstract:

    We study the behavior of the Empirical Distribution Function of iterates of intermittent maps in the Hilbert space of square integrable Functions with respect to Lebesgue measure. In the long-range dependent case, we prove that the Empirical Distribution Function, suitably normalized, converges to a degenerate stable process, and we give the corresponding almost sure result. We apply the results to the convergence of the Wasserstein distance between the Empirical measure and the invariant measure. We also apply it to obtain the asymptotic Distribution of the corresponding Cramer–von-Mises statistic.

  • Weak convergence of the Empirical process of intermittent maps in L2 under long-range dependence
    Stochastics and Dynamics, 2015
    Co-Authors: Jérôme Dedecker, Herold Dehling, Murad S Taqqu
    Abstract:

    We study the behavior of the Empirical Distribution Function of iterates of intermittent maps in the Hilbert space of square inegrable Functions with respect to Lebesgue measure. In the long-range dependent case, we prove that the Empirical Distribution Function, suitably normalized, converges to a degenerate stable process, and we give the corresponding almost sure result. We apply the results to the convergence of the Wasserstein distance between the Empirical measure and the invariant measure. We also apply it to obtain the asymptotic Distribution of the corresponding Cramér-von-Mises statistic.

  • strong approximation of the Empirical Distribution Function for absolutely regular sequences in mathbb r d
    Electronic Journal of Probability, 2014
    Co-Authors: Jérôme Dedecker, Emmanuel Rio, Florence Merlevède
    Abstract:

    We prove a strong approximation result with rates for the Empirical process associated to an absolutely regular stationary sequence of random variables with values in ${\mathbb R}^d$. As soon as the absolute regular coefficients of the sequence decrease more rapidly than $n^{1-p} $ for some $p \in ]2,3]$, we show that the error of approximation between the Empirical process and a two-parameter Gaussian process is of order $n^{1/p} (\log n)^{\lambda(d)}$ for some positive $\lambda(d)$ depending on $d$, both in ${\mathbb L}^1$ and almost surely. The power of $n$ being independent of the dimension, our results are even new in the independent setting, and improve earlier results. In addition, for absolutely regular sequences, we show that the rate of approximation is optimal up to the logarithmic term.

  • The Empirical Distribution Function for dependent variables: asymptotic and nonasymptotic results in ${\mathbb L}^p$
    ESAIM: Probability and Statistics, 2007
    Co-Authors: Jérôme Dedecker, Florence Merlevède
    Abstract:

    Considering the centered Empirical Distribution Function F n-F as a variable in , we derive non asymptotic upper bounds for the deviation of the -norms of F n-F as well as central limit theorems for the Empirical process indexed by the elements of generalized Sobolev balls. These results are valid for a large class of dependent sequences, including non-mixing processes and some dynamical systems.

  • the Empirical Distribution Function for dependent variables asymptotic and nonasymptotic results in mathbb l p
    Esaim: Probability and Statistics, 2007
    Co-Authors: Jérôme Dedecker, Florence Merlevède
    Abstract:

    Considering the centered Empirical Distribution Function F n-F as a variable in , we derive non asymptotic upper bounds for the deviation of the -norms of F n-F as well as central limit theorems for the Empirical process indexed by the elements of generalized Sobolev balls. These results are valid for a large class of dependent sequences, including non-mixing processes and some dynamical systems.

Wolfgang Wefelmeyer - One of the best experts on this subject based on the ideXlab platform.

  • estimating the error Distribution Function in semiparametric additive regression models
    Journal of Statistical Planning and Inference, 2012
    Co-Authors: Ursula U Muller, Anton Schick, Wolfgang Wefelmeyer
    Abstract:

    Abstract We consider semiparametric additive regression models with a linear parametric part and a nonparametric part, both involving multivariate covariates. For the nonparametric part we assume two models. In the first, the regression Function is unspecified and smooth; in the second, the regression Function is additive with smooth components. Depending on the model, the regression curve is estimated by suitable least squares methods. The resulting residual-based Empirical Distribution Function is shown to differ from the error-based Empirical Distribution Function by an additive expression, up to a uniformly negligible remainder term. This result implies a Functional central limit theorem for the residual-based Empirical Distribution Function. It is used to test for normal errors.

  • estimating the error Distribution Function in nonparametric regression with multivariate covariates
    Statistics & Probability Letters, 2009
    Co-Authors: Ursula U Muller, Anton Schick, Wolfgang Wefelmeyer
    Abstract:

    We consider nonparametric regression models with multivariate covariates and estimate the regression curve by an undersmoothed local polynomial smoother. The resulting residual-based Empirical Distribution Function is shown to differ from the error-based Empirical Distribution Function by the density times the average of the errors, up to a uniformly negligible remainder term. This result implies a Functional central limit theorem for the residual-based Empirical Distribution Function.

M. N. Petriev - One of the best experts on this subject based on the ideXlab platform.

  • on the Empirical Distribution Function of residuals in autoregression with outliers and pearson s chi square type tests
    Mathematical Methods of Statistics, 2018
    Co-Authors: M. V. Boldin, M. N. Petriev
    Abstract:

    We consider a stationary linear AR(p) model with observations subject to gross errors (outliers). The Distribution of outliers is unknown and arbitrary, their intensity is γn−1/2 with an unknown γ, n is the sample size. The autoregression parameters are unknown, they are estimated by any estimator which is n1/2-consistent uniformly in γ ≤ Γ < ∞. Using the residuals from the estimated autoregression, we construct a kind of Empirical Distribution Function (e.d.f.), which is a counterpart of the (inaccessible) e.d.f. of the autoregression innovations. We obtain a stochastic expansion of this e.d.f., which enables us to construct a test of Pearson’s chi-square type for testing hypotheses about the Distribution of innovations. We establish qualitative robustness of this test in terms of uniform equicontinuity of the limiting level with respect to γ in a neighborhood of γ = 0.

  • On the Empirical Distribution Function of Residuals in Autoregression with Outliers and Pearson’s Chi-Square Type Tests
    Mathematical Methods of Statistics, 2018
    Co-Authors: M. V. Boldin, M. N. Petriev
    Abstract:

    We consider a stationary linear AR(p) model with observations subject to gross errors (outliers). The Distribution of outliers is unknown and arbitrary, their intensity is γn−1/2 with an unknown γ, n is the sample size. The autoregression parameters are unknown, they are estimated by any estimator which is n1/2-consistent uniformly in γ ≤ Γ < ∞. Using the residuals from the estimated autoregression, we construct a kind of Empirical Distribution Function (e.d.f.), which is a counterpart of the (inaccessible) e.d.f. of the autoregression innovations. We obtain a stochastic expansion of this e.d.f., which enables us to construct a test of Pearson’s chi-square type for testing hypotheses about the Distribution of innovations. We establish qualitative robustness of this test in terms of uniform equicontinuity of the limiting level with respect to γ in a neighborhood of γ = 0.