Related papers: Improved Asymptotic Formulae for Statistical Inter…
We study asymptotic behaviour of stochastic approximation procedures with three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function.…
We study learning of probability distributions characterized by an unknown symmetry direction. Based on an entropic performance measure and the variational method of statistical mechanics we develop exact upper and lower bounds on the…
One of the most commonly used methods for forming confidence intervals for statistical inference is the empirical bootstrap, which is especially expedient when the limiting distribution of the estimator is unknown. However, despite its…
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…
In this paper, our interest is in the problem of simultaneous hypothesis testing when the test statistics corresponding to the individual hypotheses are possibly correlated. Specifically, we consider the case when the test statistics…
We present a general approach to constructing permutation tests that are both exact for the null hypothesis of equality of distributions and asymptotically correct for testing equality of parameters of distributions while allowing the…
Assuming that data are collected sequentially from independent streams, we consider the simultaneous testing of multiple binary hypotheses under two general setups; when the number of signals (correct alternatives) is known in advance, and…
Probabilistic specifications are fast gaining ground as a tool for statistical modeling of probabilistic systems. One of the main goals of formal methods in this domain is to ensure that specific behavior is present or absent in the system,…
Work in the classification literature has shown that in computing a classification function, one need not know the class membership of all observations in the training set; the unlabeled observations still provide information on the…
For population genetics models with recombination, obtaining an exact, analytic sampling distribution has remained a challenging open problem for several decades. Recently, a new perspective based on asymptotic series has been introduced to…
The problem of testing two simple hypotheses in a general probability space is considered. For a fixed type-I error probability, the best exponential decay rate of the type-II error probability is investigated. In regular asymptotic cases…
The theory of testing statistical functionals is developed for non-parametric two-sample problems. For differentiable real-valued statistical functionals, some tests for the one-sided and two-sided cases are proposed and studied. The…
This paper develops asymptotic theory of integrals of empirical quantile functions with respect to random weight functions, which is an extension of classical $L$-statistics. They appear when sample trimming or Winsorization is applied to…
In 1962 Dyson used a physically based, macroscopic argument to deduce the first two terms of the large spacing asymptotic expansion of the gap probability for the bulk state of random matrix ensembles with symmetry parameter \beta. In the…
This paper reviews the most common situations where one or more regularity conditions which underlie classical likelihood-based parametric inference fail. We identify three main classes of problems: boundary problems, indeterminate…
In this paper, we propose a general method for testing composite hypotheses. Our idea is to use confidence limits to define stopping and decision rules. The requirements of operating characteristic function can be satisfied by adjusting the…
Asymptotic distribution for the proportional covariance model under multivariate normal distributions is derived. To this end, the parametrization of the common covariance matrix by its Cholesky root is adopted. The derivations are made in…
Many modern statistical applications involve inference for complex stochastic models, where it is easy to simulate from the models, but impossible to calculate likelihoods. Approximate Bayesian computation (ABC) is a method of inference for…
Convergence rate estimates in limit theorems for sums of independent random variables are considered.
The likelihood function represents statistical evidence in the context of data and a probability model. Considerable theory has demonstrated that evidence strength for different parameter values can be interpreted from the ratio of…