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Cranley and Patterson put forward the following randomization as the basis for the estimation of the error of a lattice rule for an integral of a one-periodic function over the unit cube in s dimensions. The lattice rule is randomized using…
The debiased estimator is a crucial tool in statistical inference for high-dimensional model parameters. However, constructing such an estimator involves estimating the high-dimensional inverse Hessian matrix, incurring significant…
We propose a class of tests for linear regression on concomitants (induced order statistics). These tests are based on sequential sums of regression residuals. We self-center and self-normalize these sums. The resulting process is called an…
The unitary Wilson random matrix theory is an interpolation between the chiral Gaussian unitary ensemble and the Gaussian unitary ensemble. This new way of interpolation is also reflected in the orthogonal polynomials corresponding to such…
We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…
We propose the so-called jackknife empirical likelihood approach for the survey data of general unequal probability sampling designs, and analyze parameters defined according to U-statistics. We prove theoretically that jackknife…
It will be recalled that the classical bivariate normal distributions have normal marginals and normal conditionals. It is natural to ask whether a similar phenomenon can be encountered involving Poisson marginals and conditionals.…
We propose a general method for constructing hypothesis tests and confidence sets that have finite sample guarantees without regularity conditions. We refer to such procedures as "universal." The method is very simple and is based on a…
Recent likelihood theory produces $p$-values that have remarkable accuracy and wide applicability. The calculations use familiar tools such as maximum likelihood values (MLEs), observed information and parameter rescaling. The usual…
We obtain the distribution of the maximal average in a sequence of independent identically distributed exponential random variables. Surprisingly enough, it turns out that the inverse distribution admits a simple closed form. An application…
We investigate a generalized empirical likelihood approach in a two-group setting where the constraints on parameters have a form of U-statistics. In this situation, the summands that consist of the constraints for the empirical likelihood…
Fr\'echet regression extends the principles of linear regression to accommodate responses valued in generic metric spaces. While this approach has primarily focused on exploring relationships between Euclidean predictors and non-Euclidean…
We establish several optimal moment comparison inequalities (Khinchin-type inequalities) for weighted sums of independent identically distributed symmetric discrete random variables which are uniform on sets of consecutive integers.…
We consider the variance of a function of $n$ independent random variables and provide new inequalities which, in particular, extend previous results obtained for symmetric functions in the i.i.d.~setting. For instance, we obtain various…
We compute the probability distribution of the interface width at the depinning threshold, using recent powerful algorithms. It confirms the universality classes found previously. In all cases, the distribution is surprisingly well…
We obtain concentration and large deviation for the sums of independent and identically distributed random variables with heavy-tailed distributions. Our concentration results are concerned with random variables whose distributions satisfy…
We calculate and analyze various entropy measures and their properties for selected probability distributions. The entropies considered include Shannon, R\'enyi, generalized R\'enyi, Tsallis, Sharma-Mittal, and modified Shannon entropy,…
A function of the empirical characteristic function,exists for the stable distribution, which leads to a linear regression and can be used to estimate the parameters. Two approaches are often used, one to find optimal values of t, but these…
We propose and study a fully efficient method to estimate associations of an exposure with disease incidence when both, incident cases and prevalent cases, i.e. individuals who were diagnosed with the disease at some prior time point and…
For the extended skew-normal distribution, which represents an extension of the normal (or Gaussian) distribution, we focus on the properties of the log-likelihood function and derived quantities in the the bivariate case. Specifically, we…