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March 2013
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26 Reads
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2 Citations
Test
We suggest a new consistent asymptotically distribution-free test for independence of the components of bivariate random variables. The approach combines methods of order-selection tests with nonparametric copula density estimation. We deduce the asymptotic distribution of the test statistic and investigate the small sample performance by means of a simulation study and a data application.
June 2012
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116 Reads
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22 Citations
Scandinavian Journal of Statistics
. We consider a general non-parametric regression model, where the distribution of the error, given the covariate, is modelled by a conditional distribution function. For the estimation, a kernel approach as well as the (kernel based) empirical likelihood method are discussed. The latter method allows for incorporation of additional information on the error distribution into the estimation. We show weak convergence of the corresponding empirical processes to Gaussian processes and compare both approaches in asymptotic theory and by means of a simulation study.
October 2010
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3 Reads
September 2008
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48 Reads
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12 Citations
Mathematical Methods of Statistics
The aim of this paper is to show that existing estimators for the error distribution in nonparametric regression models can be improved when additional information about the distribution is included by the empirical likelihood method. The weak convergence of the resulting new estimator to a Gaussian process is shown and the performance is investigated by comparison of asymptotic mean squared errors and by means of a simulation study. As a byproduct of our proofs we obtain stochastic expansions for smooth linear estimators based on residuals from the nonparametric regression model. AMS Classification: 62G08, 62G05
November 2005
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19 Reads
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11 Citations
The aim of this paper is to show that existing estimators for the error distribution in nonparametric regression models can be improved when additional information about the distribution is included by the empirical likelihood method. The weak convergence of the resulting new estimator to a Gaussian process is shown and the performance is investigated by comparison of asymptotic mean squared errors and by means of a simulation study. As a byproduct of our proofs we obtain stochastic expansions for smooth linear estimators based on residuals from the nonparametric regression model. AMS Classification: 62G08, 62G05
... estimators as further conditions on the kernel function and bandwidth are generally required. Similar conclusions have been reached elsewhere in related literature on residual density estimation in nonparametric regression and other settings; see, e.g., Ahmad (1992), Cheng (2004), Kiwitt et al. (2008), Györfi and Walk (2012) and the discussion and references in Bott et al. (2013). ...
November 2005
... Afterwards, Ferrigno et al. (2014) established uniform asymptotic certainty bands for the CCDF using the same strategy. For a general non-parametric regression model, Kiwitt and Neumeyer (2012) set up two estimators using a kernel approch, where the distribution of the error given the covariate is modeled by a CCDF provided by P ( ≤ y|X = x). On a given compact set, Brunel (2012) and Almanjahie et al. (2018). ...
June 2012
Scandinavian Journal of Statistics
... Similar conclusions were reached in the related literature on residual density estimation in nonparametric regression and other settings; see e.g. Ahmad (1992), Cheng (2004), Kiwitt, Nagel and Neumeyer (2008), Györfi and Walk (2012), the discussion in Bott, Devroye and Kohler (2013), and references therein. ...
September 2008
Mathematical Methods of Statistics
