Related papers: Indirect Cross-validation for Density Estimation
This paper studies V-fold cross-validation for model selection in least-squares density estimation. The goal is to provide theoretical grounds for choosing V in order to minimize the least-squares loss of the selected estimator. We first…
This paper develops detailed mathematical statistical theory of a new class of cross-validation techniques of local linear kernel hazards and their multiplicative bias corrections. The new class of cross-validation combines principles of…
Compressed sensing (CS) involves sampling signals at rates less than their Nyquist rates and attempting to reconstruct them after sample acquisition. Most such algorithms have parameters, for example the regularization parameter in LASSO,…
We introduce a novel cross-validation method that we call latinCV and we compare this method to other model selection methods using data generated from a stochastic block model. Comparing latinCV to other cross-validation methods, we show…
We consider the problem of estimating the density of a random variable $X$ that can be sampled exactly by Monte Carlo (MC). We investigate the effectiveness of replacing MC by randomized quasi Monte Carlo (RQMC) or by stratified sampling…
We study the kernel estimator of the transition density of bifurcating Markov chains. Under some ergodic and regularity properties, we prove that this estimator is consistent and asymptotically normal. Next, in the numerical studies, we…
The least-squares support vector machine is a frequently used kernel method for non-linear regression and classification tasks. Here we discuss several approximation algorithms for the least-squares support vector machine classifier. The…
Estimator selection has become a crucial issue in non parametric estimation. Two widely used methods are penalized empirical risk minimization (such as penalized log-likelihood estimation) or pairwise comparison (such as Lepski's method).…
The Beta kernel estimator offers a theoretically superior alternative to the Gaussian kernel for unit interval data, eliminating boundary bias without requiring reflection or transformation. However, its adoption remains limited by the lack…
Kernel estimation techniques, such as mean shift, suffer from one major drawback: the kernel bandwidth selection. The bandwidth can be fixed for all the data set or can vary at each points. Automatic bandwidth selection becomes a real…
Estimating a distribution given access to its unnormalized density is pivotal in Bayesian inference, where the posterior is generally known only up to an unknown normalizing constant. Variational inference and Markov chain Monte Carlo…
New bandwidth selectors for kernel density estimation with directional data are presented in this work. These selectors are based on asymptotic and exact error expressions for the kernel density estimator combined with mixtures of von Mises…
In many applications, we have access to the complete dataset but are only interested in the prediction of a particular region of predictor variables. A standard approach is to find the globally best modeling method from a set of candidate…
Tuning parameter selection is of critical importance for kernel ridge regression. To this date, data driven tuning method for divide-and-conquer kernel ridge regression (d-KRR) has been lacking in the literature, which limits the…
We estimate on a compact interval densities with isolated irregularities, such as discontinuities or discontinuities in some derivatives. From independent and identically distributed observations we construct a kernel estimator with…
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 bandwidth matrix selection for kernel density estimators (KDEs) of density level sets in $\mathbb{R}^d$, $d \ge 2$. We also consider estimation of highest density regions, which differs from estimating level sets in that one…
A natural method for approximating out-of-sample predictive evaluation is leave-one-out cross-validation (LOOCV) --- we alternately hold out each case from a full data set and then train a Bayesian model using Markov chain Monte Carlo…
Variable kernel density estimation allows the approximation of a probability density by the mean of differently stretched and rotated kernels centered at given sampling points $y_n\in\mathbb{R}^d,\ n=1,\dots,N$. Up to now, the choice of the…
It is well-known that kernel regression estimators do not produce a constant estimator variance over a domain. To correct this problem, Nishida and Kanazawa (2015) proposed a variance-stabilizing (VS) local variable bandwidth for Local…