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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…
This paper presents a new perspective on the identification at infinity for the intercept of the sample selection model as identification at the boundary via a transformation of the selection index. This perspective suggests generalizations…
Weakly stationary Gaussian processes (GPs) are the principal tool in the statistical approaches to the design and analysis of computer experiments (or Uncertainty Quantification). Such processes are fitted to computer model output using a…
This work proposes a new procedure for estimating the non-stationary spatial covariance function for Spatial-Temporal Deformation. The proposed procedure is based on a monotonic function approach. The deformation functions are expanded as a…
Nonparametric kernel density and local polynomial regression estimators are very popular in Statistics, Economics, and many other disciplines. They are routinely employed in applied work, either as part of the main empirical analysis or as…
This article proposes an online bootstrap scheme for nonparametric level estimation in nonstationary time series. Our approach applies to a broad class of level estimators expressible as weighted sample averages over time windows, including…
In this paper, we present a statistical framework for modeling conditional quantiles of spatial processes assumed to be strongly mixing in space. We establish the $L_1$ consistency and the asymptotic normality of the kernel conditional…
Depth measures have gained popularity in the statistical literature for defining level sets in complex data structures like multivariate data, functional data, and graphs. Despite their versatility, integrating depth measures into…
We observe $n$ inhomogeneous Poisson processes with covariates and aim at estimating their intensities. We assume that the intensity of each Poisson process is of the form $s (\cdot, x)$ where $x$ is the covariate and where $s$ is an…
In this paper, we consider the problem of estimating the covariance kernel and its eigenvalues and eigenfunctions from sparse, irregularly observed, noise corrupted and (possibly) correlated functional data. We present a method based on…
In structural health monitoring (SHM), sensor measurements are collected, and damage-sensitive features such as natural frequencies are extracted for damage detection. However, these features depend not only on damage but are also…
Imputation is a popular technique for handling missing data. We consider a nonparametric approach to imputation using the kernel ridge regression technique and propose consistent variance estimation. The proposed variance estimator is based…
This paper considers extensions of minimum-disparity estimators to the problem of estimating parameters in a regression model that is conditionally specified; that is where a parametric model describes the distribution of a response $y$…
In the this paper, the authors propose to estimate the density of a targeted population with a weighted kernel density estimator (wKDE) based on a weighted sample. Bandwidth selection for wKDE is discussed. Three mean integrated squared…
Uncertainty quantification is essential for scientific analysis, as it allows for the evaluation and interpretation of variability and reliability in complex systems and datasets. In their original form, multivariate statistical regression…
Robust design has been widely recognized as a leading method in reducing variability and improving quality. Most of the engineering statistics literature mainly focuses on finding "point estimates" of the optimum operating conditions for…
Accurate uncertainty estimates can significantly improve the performance of iterative design of experiments, as in Sequential and Reinforcement learning. For many such problems in engineering and the physical sciences, the design task…
Self- and mutually-exciting point processes are popular models in machine learning and statistics for dependent discrete event data. To date, most existing models assume stationary kernels (including the classical Hawkes processes) and…
Given a set of points $P\subset \mathbb{R}^{d}$ and a kernel $k$, the Kernel Density Estimate at a point $x\in\mathbb{R}^{d}$ is defined as $\mathrm{KDE}_{P}(x)=\frac{1}{|P|}\sum_{y\in P} k(x,y)$. We study the problem of designing a data…
The use of covariance kernels is ubiquitous in the field of spatial statistics. Kernels allow data to be mapped into high-dimensional feature spaces and can thus extend simple linear additive methods to nonlinear methods with higher order…