Related papers: Unique Distributions Under Non-IID Assumption
Lifetime distributions of social entities, such as enterprises, products, and media contents, are one of the fundamental statistics characterizing the social dynamics. To investigate the lifetime distribution of mutually interacting…
In this paper, we study estimation of certain integral functionals of one or two densities with samples from stationary m-dependent sequences. We consider two types of U-statistic estimators for these functionals that are functions of the…
A research frontier has emerged in scientific computation, wherein numerical error is regarded as a source of epistemic uncertainty that can be modelled. This raises several statistical challenges, including the design of statistical…
This paper studies fundamental aspects of modelling data using multivariate Watson distributions. Although these distributions are natural for modelling axially symmetric data (i.e., unit vectors where $\pm \x$ are equivalent), for…
In the context of a species sampling problem we discuss a non-parametric maximum likelihood estimator for the underlying probability mass function. The estimator is known in the computer science literature as the high profile estimator. We…
Over the past decades, researchers and ML practitioners have come up with better and better ways to build, understand and improve the quality of ML models, but mostly under the key assumption that the training data is distributed…
We improve a known result on the strong consistency of M-estimates of the regression parameters in a linear model for independent and identically distributed random errors under some mild conditions.
In statistical inference, it is rarely realistic that the hypothesized statistical model is well-specified, and consequently it is important to understand the effects of misspecification on inferential procedures. When the hypothesized…
Cognitive diagnosis models have been widely used in different areas, especially intelligent education, to measure users' proficiency levels on knowledge concepts, based on which users can get personalized instructions. As the measurement is…
Outlying observations are frequently encountered across a wide spectrum of scientific domains, posing notable challenges to the generalizability of statistical models and the reproducibility of downstream analysis. They are identified…
We develop and analyze a class of unbiased Monte Carlo estimators for multivariate jump-diffusion processes with state-dependent drift, volatility, jump intensity and jump size. A change of measure argument is used to extend existing…
An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture…
The convergence of U-statistics has been intensively studied for estimators based on families of i.i.d. random variables and variants of them. In most cases, the independence assumption is crucial [Lee90, de99]. When dealing with…
In this paper we examine quantile-stratified samples from a known univariate probability distribution, with stratification occurring over a partition of the quantile regions in the distribution. We examine some general properties of this…
Multivariate extreme-value analysis is concerned with the extremes in a multivariate random sample, that is, points of which at least some components have exceptionally large values. Mathematical theory suggests the use of max-stable models…
The distribution of the spacing, or the difference between consecutive order statistics, is known only for uniform and exponential random variates. We add here logistic and Gumbel variates, and present an estimator for distributions with a…
This paper introduces Schur-constant equilibrium distribution models of dimension n for arithmetic non-negative random variables. Such a model is defined through the (several orders) equilibrium distributions of a univariate survival…
This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important…
Exponential distribution is ubiquitous in the framework of multi-agent systems. An alternative approach with an economic motivation to derive the exponential distribution in the framework of iterations in the space of distributions is…
Many works in statistics aim at designing a universal estimation procedure, that is, an estimator that would converge to the best approximation of the (unknown) data generating distribution in a model, without any assumption on this…