Exact mean and mean squared error of the smoothed bootstrap mean integrated squared error estimator

2000 ◽  
Vol 15 (2) ◽  
pp. 169-181
Author(s):  
Dominic Lee ◽  
Carey Priebe
Keyword(s):  
Mean Squared Error ◽  
Error Estimator ◽  
Mean Integrated Squared Error ◽  
Smoothed Bootstrap ◽  
Squared Error ◽  
Integrated Squared Error

scholarly journals Bootstrap Selector for the Smoothing Parameter of Beran’s Estimator

2021 ◽  
Vol 7 (1) ◽  
pp. 28
Author(s):  
Rebeca Peláez Suárez ◽  
Ricardo Cao Abad ◽  
Juan M. Vilar Fernández
Keyword(s):  
Confidence Intervals ◽  
Simulation Study ◽  
Smoothing Parameter ◽  
Bootstrap Confidence Intervals ◽  
Bootstrap Approximation ◽  
Mean Integrated Squared Error ◽  
Smoothed Bootstrap ◽  
Squared Error ◽  
Integrated Squared Error ◽  
The Mean

This work proposes a resampling technique to approximate the smoothing parameter of Beran’s estimator. It is based on resampling by the smoothed bootstrap and minimising the bootstrap approximation of the mean integrated squared error to find the bootstrap bandwidth. The behaviour of this method has been tested by simulation on several models. Bootstrap confidence intervals are also addressed in this research and their performance is analysed in the simulation study.

scholarly journals Transmetric Density Estimation

2016 ◽  
Vol 5 (2) ◽  
pp. 35
Author(s):  
Sigve Hovda
Keyword(s):  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Density ◽  
Convergence Order ◽  
Graphical Display ◽  
Mean Integrated Squared Error ◽  
Squared Error ◽  
Integrated Squared Error ◽  
The Mean ◽  
Convergence Orders

<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>

scholarly journals Exact Mean Integrated Squared Error

1992 ◽  
Vol 20 (2) ◽  
pp. 712-736 ◽  
Author(s):  
J. S. Marron ◽  
M. P. Wand
Keyword(s):  
Mean Integrated Squared Error ◽  
Squared Error ◽  
Integrated Squared Error

scholarly journals A Note on the Adaptive Estimation of a Multiplicative Separable Regression Function

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Christophe Chesneau
Keyword(s):  
Regression Model ◽  
Rate Of Convergence ◽  
Nonparametric Regression ◽  
Adaptive Estimation ◽  
Regression Function ◽  
Nonparametric Regression Model ◽  
Mean Integrated Squared Error ◽  
Squared Error ◽  
Integrated Squared Error ◽  
Separable Regression

We investigate the estimation of a multiplicative separable regression function from a bidimensional nonparametric regression model with random design. We present a general estimator for this problem and study its mean integrated squared error (MISE) properties. A wavelet version of this estimator is developed. In some situations, we prove that it attains the standard unidimensional rate of convergence under the MISE over Besov balls.

Sign in / Sign up

Export Citation Format

Share Document