Related papers: Uniform estimates for order statistics and Orlicz …
We focus on the problem of establishing the optimal upper bounds on generalized order statistics which are based on the underlying cdf belonging to the family of distributions with decreasing failure rate and decreasing failure rate on the…
We consider component-wise equivariant estimation of order restricted location/scale parameters of a general bivariate distribution under quite general conditions on underlying distributions and the loss function. This paper unifies various…
Finite sample bounds on the estimation error of the mean by the empirical mean, uniform over a class of functions, can often be conveniently obtained in terms of Rademacher or Gaussian averages of the class. If a function of n variables has…
Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous…
The joint cumulative distribution function for order statistics arising from several different populations is given in terms of the distribution function of the populations. The computational cost of the formula in the case of two…
We give estimates for the expectation of the norm of random matrices with independent but not necessarily identically distributed entries.
We obtain new sampling discretization results in Orlicz norms on finite dimensional spaces. As applications, we study sampling recovery problems, where the error of the recovery process is calculated with respect to different Orlicz norms.…
The proliferation of science and technology has led to the prevalence of voluminous data sets that are distributed across multiple machines. It is an established fact that conventional statistical methodologies may be unfeasible in the…
The assumption that the sampling distribution of the crude odds ratio (ORcrude) is a log-normal distribution with parameters mu and sigma leads to the incorrect conclusion that the expectation of the log of ORcrude is equal to the parameter…
We study the complexity of sampling, rounding, and integrating arbitrary logconcave functions. Our new approach provides the first complexity improvements in nearly two decades for general logconcave functions for all three problems, and…
Estimating the normalizing constant of an unnormalized probability distribution has important applications in computer science, statistical physics, machine learning, and statistics. In this work, we consider the problem of estimating the…
The variation of a class of Orlicz moments with respect to the Asplund sum within the class of log-concave functions is demonstrated. Such a variational formula naturally leads to a family of dual Orlicz curvature measures for log-concave…
We provide full theoretical guarantees for the convergence behaviour of diffusion-based generative models under the assumption of strongly log-concave data distributions while our approximating class of functions used for score estimation…
In the present paper, the author discusses the derivation of unit distributions and the derivation of the generalized form using the order statistics. The author discusses the Kumaraswamy as the smallest order statistic of the unit power…
Random variables equidistributed on convex bodies have received quite a lot of attention in the last few years. In this paper we prove the negative association property (which generalizes the subindependence of coordinate slabs) for…
Ordinal regression falls between discrete-valued classification and continuous-valued regression. Ordinal target variables can be associated with ranked random variables. These random variables are known as order statistics and they are…
This paper examines the local linear regression (LLR) estimate of the conditional distribution function $F(y|x)$. We derive three uniform convergence results: the uniform bias expansion, the uniform convergence rate, and the uniform…
We introduce and study deferred N\"{o}rlund statistical convergence in probability, mean of order $r,$ distribution, and study the interrelation among them. Based upon the proposed method to illustrate the findings, we present new Korovkin…
The main aim of this work is to give a general approach to the celebrated Kahane-Salem-Zygmund inequalities. We prove estimates for exponential Orlicz norms of averages $\sup_{1\le j \leq N} \big |\sum_{1 \leq i \leq K}\gamma_i(\cdot)…
In this paper, we analyze the set of all possible aggregate distributions of the sum of standard uniform random variables, a simply stated yet challenging problem in the literature of distributions with given margins. Our main results are…