Erratum to :  Calculation of the Integrated Squared Error for Systems with Time Lag

<div>A transmetric is a generalization of a metric that is tailored to properties needed in kernel density estimation. Using transmetrics in kernel density estimation is an intuitive way to make assumptions on the kernel of the distribution to improve convergence orders and to reduce the number of dimensions in the graphical display. This framework is required for discussing the estimators that are suggested by Hovda (2014).</div><div> </div><div>Asymptotic arguments for the bias and the mean integrated squared error is difficult in the general case, but some results are given when the transmetric is of the type defined in Hovda (2014). An important contribution of this paper is that the convergence order can be as high as $4/5$, regardless of the number of dimensions.</div>

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Mean integrated squared error of kernel estimators when the density and its derivative are not necessarily continuous

Annals of the Institute of Statistical Mathematics ◽

10.1007/bf02481114 ◽

1985 ◽

Vol 37 (3) ◽

pp. 461-472 ◽

Cited By ~ 31

Author(s):

Constance van Eeden

Keyword(s):

Kernel Estimators ◽

Mean Integrated Squared Error ◽

Squared Error ◽

Integrated Squared Error

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On the expansion of the mean integrated squared error of a kernel density estimator

Statistics & Probability Letters ◽

10.1016/s0167-7152(01)00032-3 ◽

2001 ◽

Vol 52 (4) ◽

pp. 441-450 ◽

Cited By ~ 3

Author(s):

Bert van Es

Keyword(s):

Kernel Density ◽

Kernel Density Estimator ◽

Density Estimator ◽

Mean Integrated Squared Error ◽

Squared Error ◽

Integrated Squared Error ◽

The Mean

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New Bandwidth Selection for Kernel Quantile Estimators

Journal of Probability and Statistics ◽

10.1155/2012/138450 ◽

2012 ◽

Vol 2012 ◽

pp. 1-18

Author(s):

Ali Al-Kenani ◽

Keming Yu

Keyword(s):

Cross Validation ◽

Kernel Smoothing ◽

Bandwidth Selection ◽

Unbiased Estimation ◽

Optimal Bandwidth ◽

Squared Error ◽

Bandwidth Parameter ◽

Integrated Squared Error ◽

Selection For ◽

Quantile Estimators

We propose a cross-validation method suitable for smoothing of kernel quantile estimators. In particular, our proposed method selects the bandwidth parameter, which is known to play a crucial role in kernel smoothing, based on unbiased estimation of a mean integrated squared error curve of which the minimising value determines an optimal bandwidth. This method is shown to lead to asymptotically optimal bandwidth choice and we also provide some general theory on the performance of optimal, data-based methods of bandwidth choice. The numerical performances of the proposed methods are compared in simulations, and the new bandwidth selection is demonstrated to work very well.

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