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>

NONLINEAR WAVELET ESTIMATION OF CONDITIONAL DENSITY UNDER LEFT-TRUNCATED AND α-MIXING ASSUMPTIONS

2011 ◽  
Vol 09 (06) ◽  
pp. 989-1023 ◽  
Author(s):  
SI-LI NIU ◽  
HAN-YING LIANG
Keyword(s):  
Asymptotic Expression ◽  
Kernel Estimator ◽  
Conditional Density ◽  
Left Truncation ◽  
Mean Integrated Squared Error ◽  
Wavelet Estimator ◽  
Squared Error ◽  
Integrated Squared Error ◽  
The Mean ◽  
Mixing Sequence

In this paper, we construct a nonlinear wavelet estimator of conditional density function for a left truncation model. We provide an asymptotic expression for the mean integrated squared error (MISE) of the estimator. It is assumed that the lifetime observations form a stationary α-mixing sequence. Unlike for kernel estimator, the MISE expression of the nonlinear wavelet estimator is not affected by the presence of discontinuities in the curves.

scholarly journals A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator underα-Mixing Dependence

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Christophe Chesneau
Keyword(s):  
Density Estimation ◽  
General Setting ◽  
Type Model ◽  
Hard Thresholding ◽  
Mean Integrated Squared Error ◽  
Wavelet Estimator ◽  
Squared Error ◽  
Integrated Squared Error ◽  
The Mean ◽  
Weakly Dependent Data

We consider the estimation of an unknown functionffor weakly dependent data (α-mixing) in a general setting. Our contribution is theoretical: we prove that a hard thresholding wavelet estimator attains a sharp rate of convergence under the mean integrated squared error (MISE) over Besov balls without imposing too restrictive assumptions on the model. Applications are given for two types of inverse problems: the deconvolution density estimation and the density estimation in a GARCH-type model, both improve existing results in this dependent context. Another application concerns the regression model with random design.

scholarly journals The change in estimate method for selecting confounders: A simulation study

2021 ◽  
pp. 096228022110342
Author(s):  
Denis Talbot ◽  
Awa Diop ◽  
Mathilde Lavigne-Robichaud ◽  
Chantal Brisson
Keyword(s):  
Confidence Intervals ◽  
Simulation Study ◽  
Mean Squared Error ◽  
Real Data ◽  
Significance Test ◽  
Simulation Studies ◽  
Squared Error ◽  
Estimate Method ◽  
The Mean ◽  
Work And Health

Background The change in estimate is a popular approach for selecting confounders in epidemiology. It is recommended in epidemiologic textbooks and articles over significance test of coefficients, but concerns have been raised concerning its validity. Few simulation studies have been conducted to investigate its performance. Methods An extensive simulation study was realized to compare different implementations of the change in estimate method. The implementations were also compared when estimating the association of body mass index with diastolic blood pressure in the PROspective Québec Study on Work and Health. Results All methods were susceptible to introduce important bias and to produce confidence intervals that included the true effect much less often than expected in at least some scenarios. Overall mixed results were obtained regarding the accuracy of estimators, as measured by the mean squared error. No implementation adequately differentiated confounders from non-confounders. In the real data analysis, none of the implementation decreased the estimated standard error. Conclusion Based on these results, it is questionable whether change in estimate methods are beneficial in general, considering their low ability to improve the precision of estimates without introducing bias and inability to yield valid confidence intervals or to identify true confounders.

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