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

1985 ◽  
Vol 37 (3) ◽  
pp. 461-472 ◽  
Author(s):  
Constance van Eeden
Keyword(s):  
Kernel Estimators ◽  
Mean Integrated Squared Error ◽  
Squared Error ◽  
Integrated Squared Error

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.

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 On bagging and estimation in multivariate mixtures

2008 ◽  
Vol 5 (1) ◽  
Author(s):  
Reza Pakyari
Keyword(s):  
Monte Carlo ◽  
Standard Deviation ◽  
Maximum Likelihood ◽  
Real Data ◽  
Likelihood Estimator ◽  
Mean Integrated Squared Error ◽  
Squared Error ◽  
Absolute Bias ◽  
Integrated Squared Error ◽  
Mixing Proportion

Two bagging approaches, say \(\frac{1}{2}n\)-out-of-\(n\) without replacement (subagging) and \(n\)-out-of-\(n\) with replacement (bagging) have been applied in the problem of estimation of the parameters in a multivariate mixture model. It has been observed by Monte Carlo simulations and a real data example, that both bagging methods have improved the standard deviation of the maximum likelihood estimator of the mixing proportion, whilst the absolute bias increased slightly. In estimating the component distributions, bagging could increase the root mean integrated squared error when estimating the most probable component.

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