Related papers: Delta method in large deviations and moderate devi…
We consider the problem of allocating samples to a finite set of discrete distributions in order to learn them uniformly well in terms of four common distance measures: $\ell_2^2$, $\ell_1$, $f$-divergence, and separation distance. To…
The small-ball method was introduced as a way of obtaining a high probability, isomorphic lower bound on the quadratic empirical process, under weak assumptions on the indexing class. The key assumption was that class members satisfy a…
We study the empirical version of halfspace depths with the objective of establishing a connection between the rates of convergence and the tail behaviour of the corresponding underlying distributions. The intricate interplay between the…
Measurement error is a pervasive issue which renders the results of an analysis unreliable. The measurement error literature contains numerous correction techniques, which can be broadly divided into those which aim to produce exactly…
In this paper we consider the estimation problem for high quantiles of a heavy-tailed distribution from block data when only a few largest values are observed within blocks. We propose estimators for high quantiles and prove that these…
This study presents new closed-form estimators for the Dirichlet and the Multivariate Gamma distribution families, whose maximum likelihood estimator cannot be explicitly derived. The methodology builds upon the score-adjusted estimators…
A Cram\'er-type moderate deviation theorem quantifies the relative error of the tail probability approximation. It provides theoretical justification when the limiting tail probability can be used to estimate the tail probability under…
To measure the degree of agreement between two observers that independently classify $n$ subjects within $K$ categories, it is common to use different kappa type coefficients, the most common of which is the $\kappa_C$ coefficient (Cohen's…
We are concerned with obtaining well-calibrated output distributions from regression models. Such distributions allow us to quantify the uncertainty that the model has regarding the predicted target value. We introduce the novel concept of…
This paper focuses on nonparametric statistical inference of the hazard rate function of discrete distributions based on $\delta$-record data. We derive the explicit expression of the maximum likelihood estimator and determine its exact…
Ewens-Pitman model has been successfully applied to various fields including Bayesian statistics. There are four important estimators $K_{n},M_{l,n}$,$K_{m}^{(n)},M_{l,m}^{(n)}$. In particular, $M_{1,n}, M_{1,m}^{(n)}$ are related to…
A new approach of obtaining stratified random samples from statistically dependent random variables is described. The proposed method can be used to obtain samples from the input space of a computer forward model in estimating expectations…
For a random variable $X$, we are interested in the blind extraction of its finest mutual independence pattern $\mu ( X )$. We introduce a specific kind of independence that we call dichotomic. If $\Delta ( X )$ stands for the set of all…
This study develops a non-asymptotic Gaussian approximation theory for distributions of M-estimators, which are defined as maximizers of empirical criterion functions. In existing mathematical statistics literature, numerous studies have…
Stein's method compares probability distributions through the study of a class of linear operators called Stein operators. While mainly studied in probability and used to underpin theoretical statistics, Stein's method has led to…
Many practical problems are related to the pointwise estimation of dis- tribution functions when data contains measurement errors. Motivation for these problems comes from diverse fields such as astronomy, reliability, quality control,…
This paper presents a new variational data assimilation (VDA) approach for the formal treatment of bias in both model outputs and observations. This approach relies on the Wasserstein metric stemming from the theory of optimal mass…
We introduce a trimmed version of the Hill estimator for the index of a heavy-tailed distribution, which is robust to perturbations in the extreme order statistics. In the ideal Pareto setting, the estimator is essentially finite-sample…
This paper considers distributed statistical inference for general symmetric statistics %that encompasses the U-statistics and the M-estimators in the context of massive data where the data can be stored at multiple platforms in different…
This paper proposes a novel test method for high-dimensional mean testing regard for the temporal dependent data. Comparison to existing methods, we establish the asymptotic normality of the test statistic without relying on restrictive…