Nonparametric Kernel Distribution Function Estimation with<b>kerdiest</b>: An<i>R</i>Package for Bandwidth Choice and Applications

Quintela-del-Rı́o, Alejandro; Estévez-Pérez, Graciela

doi:10.18637/jss.v050.i08

Cited by 32 publications

(18 citation statements)

References 28 publications

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“…In Figure we compare

{\overset{J}{true}}_{n, m} false(x false)

to the true function J m ( x ) for different transformations G ( x ). For the smoothing we have used the R‐package kerdiest, see also Quintela‐del‐Rio and Estevez‐Perez (). By Theorem 2.9 there are lots of possible combinations of the smoothing bandwidth h n , the block length l and the number of drawn blocks p .…”

Section: Resultsmentioning

confidence: 99%

Block Bootstrap for the Empirical Process of Long‐Range Dependent Data

Tewes

2017

Journal Time Series Analysis

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We consider the bootstrapped empirical process of long-range dependent data. It is shown that this process converges to a semi-degenerate limit, where the random part of this limit is always Gaussian. Thus the bootstrap might fail when the original empirical process accomplishes a noncentral limit theorem. However, even in this case our results can be used to estimate a nuisance parameter that appears in the limit of many nonparametric tests under long memory. Moreover, we develop a new resampling procedure for goodness-of-fit tests and a test for monotonicity of transformations.

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“…In Figure we compare

{\overset{J}{true}}_{n, m} false(x false)

Section: Resultsmentioning

confidence: 99%

Block Bootstrap for the Empirical Process of Long‐Range Dependent Data

Tewes

2017

Journal Time Series Analysis

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“…The range, quartile range and standard deviation of the mean and amplitude of each load set are shown in Table 2. The evaluation matrix R is established according to (19)…”

Section: Case Study and Discussionmentioning

confidence: 99%

“…After selecting suitable bandwidth and kernel function [19,20], PDF of the load data can be estimated effectively.…”

Section: Epanechnikov Kernel Functionmentioning

confidence: 99%

Selection Method for Kernel Function in Nonparametric Extrapolation Based on Multicriteria Decision-Making Technology

Wang

Liu

Zeng

et al. 2013

Mathematical Problems in Engineering

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Selecting the most appropriate kernel function to extrapolate a load set is the paramount step in compiling load spectrum, as it affects the results of nonparametric extrapolation largely. Aiming at this issue, this paper provides a new approach in selecting kernel function for the nonparametric extrapolation. To solve the complexity and uncertainty of nonparametric extrapolation, characteristics of four kernel functions and their effects on the results are explained in the “from-to” diagram obtained by rainflow counting. Multicriteria decision-making (MCDM) is then applied to solve the selection problem of kernel function. To evaluate the dispersion degrees of the mean and amplitude of a load set accurately, their range, standard deviation, and interquartile range are selected as the evaluation criteria. The weight of each criterion, which represents the impact degree on the selection of the kernel function, is calculated separately using the eigenvector and entropy method. The comprehensive weights are obtained by applying the optimization theory and Jaynes’ maximum entropy principle. Finally, the importance of each criterion is discussed according to their calculated comprehensive weights, and the selection method for kernel functions is obtained, which is illustrated by extrapolating the output torque of the power split device of hybrid electrical vehicles.

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“…If the bandwidth is small, we will obtain an under-smoothed estimator, with high variability. On the contrary, if the value of h is big, the resulting estimator will be very smooth and farther from the function that we are trying to estimate [23](see figure 1). Table 1.…”

Section: Copula Function Estimationmentioning

confidence: 94%