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The effect of uncertainties and noise on a quantity of interest (model output) is often better described by its probability density function (PDF) than by its moments. Although density estimation is a common task, the adequacy of…
Skewness is a common occurrence in statistical applications. In recent years, various distribution families have been proposed to model skewed data by introducing unequal scales based on the median or mode. However, we argue that the point…
Subsampling algorithms for various parametric regression models with massive data have been extensively investigated in recent years. However, all existing studies on subsampling heavily rely on clean massive data. In practical…
The computation of scientific data can be very time consuming even if they are ultimately determined by a small number of parameters. The principle of compressed sampling suggests that we can achieve a considerable decrease in the…
In areas such as kernel smoothing and non-parametric regression there is emphasis on smooth interpolation and smooth statistical models. Splines are known to have optimal smoothness properties in one and higher dimensions. It is shown, with…
Nonparametric estimation of copula density functions using kernel estimators presents significant challenges. One issue is the potential unboundedness of certain copula density functions at the corners of the unit square. Another is the…
B-spline models are a powerful way to represent scientific data sets with a functional approximation. However, these models can suffer from spurious oscillations when the data to be approximated are not uniformly distributed. Model…
Propensity score matching has been a long-standing tradition for handling confounding in causal inference, however requiring stringent model assumptions. In this article, we propose double score matching(DSM) for general causal estimands…
A random Gaussian density field contains a fixed amount of Fisher information on the amplitude of its power spectrum. For a given smoothing scale, however, that information is not evenly distributed throughout the smoothed field. We…
Stochastic Neighbor Embedding (SNE) methods minimize the divergence between the similarity matrix of a high-dimensional data set and its counterpart from a low-dimensional embedding, leading to widely applied tools for data visualization.…
M-type smoothing splines are a broad class of spline estimators that include the popular least-squares smoothing spline but also spline estimators that are less susceptible to outlying observations and model-misspecification. However,…
Large samples have been generated routinely from various sources. Classic statistical models, such as smoothing spline ANOVA models, are not well equipped to analyze such large samples due to expensive computational costs. In particular,…
This paper investigates the double descent phenomenon in two-layer neural networks, focusing on the role of L1 regularization and representation dimensions. It explores an alternative double descent phenomenon, named sparse double descent.…
With large-scale database systems, statistical analysis of data, formed by probability distributions, become an important task in explorative data analysis. Nevertheless, due to specific properties of density functions, their proper…
Residual errors in shear measurements, after corrections for instrument systematics and atmospheric effects, can impact cosmological parameters derived from weak lensing observations. Here we combine convergence maps from our suite of…
In this paper, we develop a method for estimating and clustering two-dimensional spectral density functions (2D-SDFs) for spatial data from multiple subregions. We use a common set of adaptive basis functions to explain the similarities…
We study the maximum smoothed likelihood estimator (MSLE) for interval censoring, case 2, in the so-called separated case. Characterizations in terms of convex duality conditions are given and strong consistency is proved. Moreover, we show…
Computational capability often falls short when confronted with massive data, posing a common challenge in establishing a statistical model or statistical inference method dealing with big data. While subsampling techniques have been…
Nested sampling has emerged as a valuable tool for Bayesian analysis, in particular for determining the Bayesian evidence. The method is based on a specific type of random sampling of the likelihood function and prior volume of the…
This paper deals with the problem of estimating a slope parameter in a simple linear regression model, where independent variables have functional measurement errors. Measurement errors in independent variables, as is well known, cause…