相关论文: Bandwidth choice for nonparametric classification
A new method of bandwidth selection for kernel density estimators is proposed. The method, termed indirect cross-validation, or ICV, makes use of so-called selection kernels. Least squares cross-validation (LSCV) is used to select the…
In the context of kernel density estimation, we give a characterization of the kernels for which the parametric mean integrated squared error rate $n^{-1}$ may be obtained, where $n$ is the sample size. Also, for the cases where this rate…
In this work, we investigate the statistical computation of the Boltzmann entropy of statistical samples. For this purpose, we use both histogram and kernel function to estimate the probability density function of statistical samples. We…
A popular data-driven method for choosing the bandwidth in standard kernel regression is cross-validation. Even when there are outliers in the data, robust kernel regression can be used to estimate the unknown regression curve [Robust and…
Adaptive bandwidth selection is a fundamental challenge in nonparametric regression. This paper introduces a new bandwidth selection procedure inspired by the optimality criteria for $\ell_0$-penalized regression. Although similar in spirit…
A new plug-in rule procedure for bandwidth selection in kernel circular density estimation is introduced. The performance of this proposal is checked throughout a simulation study considering a variety of circular distributions exhibiting…
We consider the problem of learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights. We consider the asymptotic limit where the number of samples, the input dimension and…
We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…
We investigate the asymptotic mean squared error of kernel estimators of the intensity function of a spatial point process. We show that when $n$ independent copies of a point process in $\mathbb R^d$ are superposed, the optimal bandwidth…
This paper proposes a new method of bandwidth selection in kernel estimation of density and distribution functions motivated by the connection between maximisation of the entropy of probability integral transforms and maximum likelihood in…
Weight quantization for deep ConvNets has shown promising results for applications such as image classification and semantic segmentation and is especially important for applications where memory storage is limited. However, when aiming for…
We study the asymptotic behavior of least-squares cross-validation bandwidth selection in kernel density estimation on the $d$-dimensional hypersphere, $d\geq 1$. We show that the exact rate of convergence with respect to the optimal…
Given a sample $\{X_i\}_{i=1}^n$ from $f_X$, we construct kernel density estimators for $f_Y$, the convolution of $f_X$ with a known error density $f_{\epsilon}$. This problem is known as density estimation with Berkson error and has…
In this paper, we consider the problem of estimating a conditional density in moderately large dimensions. Much more informative than regression functions, conditional densities are of main interest in recent methods, particularly in the…
Kernel-based estimators such as local polynomial estimators in regression discontinuity designs are often evaluated at multiple bandwidths as a form of sensitivity analysis. However, if in the reported results, a researcher selects the…
Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of…
Recent contributions to kernel smoothing show that the performance of cross-validated bandwidth selectors improve significantly from indirectness. Indirect crossvalidation first estimates the classical cross-validated bandwidth from a more…
Averaging provides an alternative to bandwidth selection for density kernel estimation. We propose a procedure to combine linearly several kernel estimators of a density obtained from different, possibly data-driven, bandwidths. The method…
This paper develops a novel approach to density estimation on a network. We formulate nonparametric density estimation on a network as a nonparametric regression problem by binning. Nonparametric regression using local polynomial…
It is well known that the number of modes of a kernel density estimator is monotone nonincreasing in the bandwidth if the kernel is a Gaussian density. There is numerical evidence of nonmonotonicity in the case of some non-Gaussian kernels,…