Bandwidth Selection in Nonparametric Kernel Testing

Gao, Jiti; Gijbels, Irène

doi:10.1198/016214508000000968

Cited by 123 publications

(69 citation statements)

References 40 publications

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“…Herrmann et al (1992) and Wu & Zhao (2007) dealt with models with stationary errors. Hall & Hart (1990), Kulasekera & Wang (1997) and Gao & Gijbels (2008) considered bandwidth selection in the context of nonparametric 175 hypothesis testing. We propose using the asymptotic mean squared error optimal bandwidth b n = cn −1/5 , where c > 0 is a constant.…”

Section: ·5 Bandwidth Selectionmentioning

confidence: 99%

Testing parametric assumptions of trends of a nonstationary time series

Zhang

2011

Biometrika

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SUMMARYThe paper considers testing whether the mean trend of a nonstationary time series is of certain parametric forms. A central limit theorem for the integrated squared error is derived, and with that a hypothesis-testing procedure is proposed. The method is illustrated in a simulation study, and is applied to assess the mean pattern of lifetime-maximum wind speeds of global tropical cyclones from 1981 to 2006. We also revisit the trend pattern in the central England temperature series.

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Section: ·5 Bandwidth Selectionmentioning

confidence: 99%

Testing parametric assumptions of trends of a nonstationary time series

Zhang

2011

Biometrika

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“…The second way is given by an adaptive-rate-optimal rule proposed by Horowitz and Spokoiny (2001) for testing a parametric model for conditional mean function against a nonparametric alternative. The third way for selecting a practical bandwidth is introduced by Gao and Gijbels (2008). Gao and Gijbels (2008) propose, using the Edgeworth expansion of the asymptotic distribution of the test, to choose the bandwidth such that the power function of the test is maximized while the size function is controlled.…”

Section: Monte Carlo Simulations: Size and Powermentioning

confidence: 99%

“…The third way for selecting a practical bandwidth is introduced by Gao and Gijbels (2008). Gao and Gijbels (2008) propose, using the Edgeworth expansion of the asymptotic distribution of the test, to choose the bandwidth such that the power function of the test is maximized while the size function is controlled. The above three approaches will be investigated in future research.…”

Section: Monte Carlo Simulations: Size and Powermentioning

confidence: 99%

Nonparametric tests for conditional independence using conditional distributions

Bouezmarni

Taamouti

2014

Journal of Nonparametric Statistics

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The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. ABSTRACTThe concept of causality is naturally defined in terms of conditional distribution, however almost all the empirical works focus on causality in mean. This paper aims to propose a nonparametric statistic to test the conditional independence and Granger non-causality between two variables conditionally on another one. The test statistic is based on the comparison of conditional distribution functions using an L 2 metric. We use Nadaraya-Watson method to estimate the conditional distribution functions. We establish the asymptotic size and power properties of the test statistic and we motivate the validity of the local bootstrap. We ran a simulation experiment to investigate the finite sample properties of the test and we illustrate its practical relevance by examining the Granger non-causality between S&P 500 Index returns and VIX volatility index. Contrary to the conventional t-test which is based on a linear mean-regression, we find that VIX index predicts excess returns both at short and long horizons.

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“…This corresponds to selecting h by maximizing estimated power. See Doksum and Schafer [5], Gao and Gijbels [7], Doksum et al [3], Schafer and Doksum [16].…”

Section: Numerical Predictor: Local Contingency Efficacymentioning

confidence: 99%

Nonparametric variable selection and classification: The CATCH algorithm

Tang

Chen

Tsui

et al. 2014

Computational Statistics & Data Analysis

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In a nonparametric framework, we consider the problem of classifying a categorical response Y whose distribution depends on a vector of predictors X, where the coordinates X j of X may be continuous, discrete, or categorical. To select the variables to be used for classification, we construct an algorithm which for each variable X j computes an importance score s j to measure the strength of association of X j with Y . The algorithm deletes X j if s j falls below a certain threshold. It is shown in Monte Carlo simulations that the algorithm has a high probability of only selecting variables associated with Y . Moreover when this variable selection rule is used for dimension reduction prior to applying classification procedures, it improves the performance of these procedures. Our approach for computing importance scores is based on root Chisquare type statistics computed for randomly selected regions (tubes) of the sample space. The size and shape of the regions are adjusted iteratively and adaptively using the data to enhance the ability of the importance score to detect local relationships between the response and the predictors. These local scores are then averaged over the tubes to form a global importance score s j for variable X j . When confounding and spurious associations are issues, the nonparametric importance score for variable X j is computed conditionally by using tubes to restrict the other variables . We call this variable selection procedure CATCH (Categorical Adaptive Tube Covariate Hunting). We establish asymptotic properties, including consistency.

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Bandwidth Selection in Nonparametric Kernel Testing

Cited by 123 publications

References 40 publications

Testing parametric assumptions of trends of a nonstationary time series

Testing parametric assumptions of trends of a nonstationary time series

Nonparametric tests for conditional independence using conditional distributions

Nonparametric variable selection and classification: The CATCH algorithm

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