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In this paper, we propose a random projection approach to estimate variance in kernel ridge regression. Our approach leads to a consistent estimator of the true variance, while being computationally more efficient. Our variance estimator is…
This work considers the subdiffusion problem with non-positive memory, which not only arises from physical laws with memory, but could be transformed from sophisticated models such as subdiffusion or subdiffusive Fokker-Planck equation with…
Key to effective generic, or "black-box", variational inference is the selection of an approximation to the target density that balances accuracy and speed. Copula models are promising options, but calibration of the approximation can be…
Kernel methods are an important class of techniques in machine learning. To be effective, good feature maps are crucial for mapping non-linearly separable input data into a higher dimensional (feature) space, thus allowing the data to be…
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 $y$…
We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The…
In this paper we consider the kernel estimators of a distribution function defined by the stochastic approximation algorithm when the observation are contamined by measurement errors. It is well known that this estimators depends heavily on…
We estimate the derivative of a probability density function defined on $[0,\infty)$. For this purpose, we choose the class of kernel estimators with asymmetric gamma kernel functions. The use of gamma kernels is fruitful due to the fact…
Generative models, like large language models, are becoming increasingly relevant in our daily lives, yet a theoretical framework to assess their generalization behavior and uncertainty does not exist. Particularly, the problem of…
In this paper, we identify the criteria for the selection of the minimal and most efficient covariate adjustment sets for the regression calibration method developed by Carroll, Rupert and Stefanski (CRS, 1992), used to correct bias due to…
The evaluation of image generators remains a challenge due to the limitations of traditional metrics in providing nuanced insights into specific image regions. This is a critical problem as not all regions of an image may be learned with…
Modeling and estimation for spatial data are ubiquitous in real life, frequently appearing in weather forecasting, pollution detection, and agriculture. Spatial data analysis often involves processing datasets of enormous scale. In this…
We consider the high order moments estimator of the frontier of a random pair introduced by Girard, S., Guillou, A., Stupfler, G. (2012). {\it Frontier estimation with kernel regression on high order moments}. In the present paper, we show…
Lensing peaks have been proposed as a useful statistic, containing cosmological information from non-Gaussianities that is inaccessible from traditional two-point statistics such as the power spectrum or two-point correlation functions.…
In statistics permutations typically arise in the context of rank plots for two-dimensional data. Such plots can also be interpreted as discrete copulas. In discrete mathematics, typically in the context of the description of large…
We consider the problem of estimating a regression function when a covariate is measured with error. Using the local polynomial estimator of Delaigle, Fan, and Carroll (2009) as a benchmark, we propose an alternative way of solving the…
We introduce novel information-theoretic measures termed the multivariate cumulative copula fractional inaccuracy measure and the multivariate survival copula fractional inaccuracy measure, constructed respectively from multivariate copulas…
We propose new estimates for the frontier of a set of points. They are defined as kernel estimates covering all the points and whose associated support is of smallest surface. The estimates are written as linear combinatio- ns of kernel…
We present an effective framework for improving the breakdown point of robust regression algorithms. Robust regression has attracted widespread attention due to the ubiquity of outliers, which significantly affect the estimation results.…
In this work, we propose a mean-squared error-based risk that enables the comparison and optimization of estimators of squared calibration errors in practical settings. Improving the calibration of classifiers is crucial for enhancing the…