Related papers: Generalized R\'enyi statistics
High-dimensional covariance estimation is notoriously sensitive to outliers. While statistically optimal estimators exist for general heavy-tailed distributions, they often rely on computationally expensive techniques like semidefinite…
In this survey we present an extensive research of the vast literature about the Generalized Lambda Distribution (GLD) and propose a hurdle, or two-way, model whose associated distribution is the GLD in order to meet the demand for a highly…
Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…
We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the…
We explore some properties of the conditional distribution of an i.i.d. sample under large exceedances of its sum. Thresholds for the asymptotic independance of the summands are observed, in contrast with the classical case when the…
R\'enyi transfer entropy (RTE) is a generalization of classical transfer entropy that replaces Shannon's entropy with R\'enyi's information measure. This, in turn, introduces a new tunable parameter $\alpha$, which accounts for sensitivity…
We consider Gini's mean difference statistic as an alternative to the empirical variance in the settings of finite populations where simple random samples are drawn without replacement. In particular, we discuss specific (in the finite…
Existing sequential generalized estimating equation methodology for longitudinal and group-correlated data focuses on narrow hypotheses concerning treatment efficacy and often makes modeling assumptions that impede the desirable robustness…
In this article we discuss estimation of the common variance of several normal populations with tree order restricted means. We discuss the asymptotic properties of the maximum likelihood estimator of the variance as the number of…
Parameters defined via general estimating equations (GEE) can be estimated by maximizing the empirical likelihood (EL). Newey and Smith [Econometrica 72 (2004) 219--255] have recently shown that this EL estimator exhibits desirable…
A recent article on generalised linear mixed model asymptotics, Jiang et al. (2022), derived the rates of convergence for the asymptotic variances of maximum likelihood estimators. If $m$ denotes the number of groups and $n$ is the average…
In this paper we propose a new lifetime model, called the odd generalized exponential linear failure rate distribution. Some statistical properties of the proposed distribution such as the moments, the quantiles, the median, and the mode…
Competing styles of Statistical Mechanics have been introduced as practical succedaneous to the conventional well established Boltzmann-Gibbs statistical mechanics, when in the use of the latter the researcher is impaired in his/her…
Taylor's law, also known as fluctuation scaling in physics and the power-law variance function in statistics, is an empirical pattern widely observed across fields including ecology, physics, finance, and epidemiology. It states that the…
Let $X_{1},\ldots ,X_{n}$ be $n$ real-valued dependent random variables. With motivation from Mitra and Resnick (2009), we derive the tail asymptotic expansion for the weighted sum of order statistics $X_{1:n}\leq \cdots \leq X_{n:n}$ of…
In this paper we extend the work of Owen (2007) by deriving a second order expansion for the slope parameter in logistic regression, when the size of the majority class is unbounded and the minority class is finite. More precisely, we…
Statistical evaluation aims to estimate the generalization performance of a model using held-out i.i.d.\ test data sampled from the ground-truth distribution. In supervised learning settings such as classification, performance metrics such…
The R\'{e}nyi cross-entropy measure between two distributions, a generalization of the Shannon cross-entropy, was recently used as a loss function for the improved design of deep learning generative adversarial networks. In this work, we…
There is accumulating evidence in the literature that stability of learning algorithms is a key characteristic that permits a learning algorithm to generalize. Despite various insightful results in this direction, there seems to be an…
A powerful robust mean estimator introduced by Catoni (2012) allows for mean estimation of heavy-tailed data while achieving the performance characteristics of classical mean estimator for sub-Gaussian data. While Catoni's framework has…