Related papers: Moment-based density and risk estimation from grou…
First, we present a concise glossary of formulas for composition of standard, cumulant, factorial, and factorial cumulant moments in superposition (compound) models, where final particles are created via independent emission from a…
The purpose of the present paper is to establish moment estimates of Rosenthal type for a rather general class of random variables satisfying certain bounds on the cumulants. We consider sequences of random variables which satisfy a central…
A Bayesian method of moments/instrumental variable (BMOM/IV) approach is developed and applied in the analysis of the important mean and multiple regression models. Given a single set of data, it is shown how to obtain posterior and…
Nonparametric estimators for the mean and the covariance functions of functional data are proposed. The setup covers a wide range of practical situations. The random trajectories are, not necessarily differentiable, have unknown regularity,…
Recent work suggests that some auto-encoder variants do a good job of capturing the local manifold structure of the unknown data generating density. This paper contributes to the mathematical understanding of this phenomenon and helps…
We investigate the parameter estimation of regression models with fixed group effects, when the group variable is missing while group related variables are available. This problem involves clustering to infer the missing group variable…
One of the popular measures of central tendency that provides better representation and interesting insights of the data compared to the other measures like mean and median is the metric mode. If the analytical form of the density function…
Mixture models are a fundamental tool in applied statistics and machine learning for treating data taken from multiple subpopulations. The current practice for estimating the parameters of such models relies on local search heuristics…
In many applications, data cluster. Failing to take the cluster structure into consideration generally leads to underestimated variances of point estimators and inflated type I errors in hypothesis tests. Many circumstance-dependent…
Grouped data are commonly encountered in applications. The Bernstein polynomial model is proposed as an approximate model in this paper for estimating a univariate density function based on grouped data. The coefficients of the Bernstein…
Dealing with visualizations containing large data set is a challenging issue and, in the field of Information Visualization, almost every visual technique reveals its drawback when visualizing large number of items. To deal with this…
Central moments and cumulants are often employed to characterize the distribution of data. The skewness and kurtosis are particularly useful for the detection of outliers, the assessment of departures from normally distributed data,…
The concept of biased data is well known and its practical applications range from social sciences and biology to economics and quality control. These observations arise when a sampling procedure chooses an observation with probability that…
In reliability theory and survival analysis, observed data are often weakly dependent and subject to additive measurement errors. Such contamination arises when the underlying data are neither independent nor strongly mixed but instead…
This study addresses the reliability of automatic summarization in high-risk scenarios and proposes a large language model framework that integrates uncertainty quantification and risk-aware mechanisms. Starting from the demands of…
Nonparametric density estimation is considered for a discretely observed stationary continuous-time process. For each of three given time sampling procedures either random or deterministic, we establish that histograms and frequency…
Finite mixture of Gaussian distributions provide a flexible semi-parametric methodology for density estimation when the variables under investigation have no boundaries. However, in practical applications variables may be partially bounded…
This paper deals with a general class of transformation models that contains many important semiparametric regression models as special cases. It develops a self-induced smoothing for the maximum rank correlation estimator, resulting in…
This study enhances a crowd density estimation algorithm originally designed for image-based analysis by adapting it for video-based scenarios. The proposed method integrates a denoising probabilistic model that utilizes diffusion processes…
We describe and analyze a broad class of mixture models for real-valued multivariate data in which the probability density of observations within each component of the model is represented as an arbitrary combination of basis functions.…