Related papers: Optimal sequential tests yield log-optimal e-proce…

Confidence sequences based on test martingales provide time-uniform uncertainty quantification for the mean of bounded IID observations without parametric distributional assumptions. Their practical efficiency, however, depends strongly on…

Many problems in quantum information theory can be formulated as optimizations over the sequential outcomes of dynamical systems subject to unpredictable external influences. Such problems include many-body entanglement detection through…

This work is an extension in Arch models of the theorem of S.Y. Hwang and I.V. Basawa Hwang and Basawa (2001) which was used before in nonlinear time series contiguous to AR(1) processes. Our results are established under some general…

We propose a new sequential monitoring scheme for changes in the parameters of a multivariate time series. In contrast to procedures proposed in the literature which compare an estimator from the training sample with an estimator calculated…

Augmenting test suites with test cases that reflect the actual usage of the software system is extremely important to sustain the quality of long lasting software systems. In this paper, we propose E-Test, an approach that incrementally…

Although the assumption of elliptical symmetry is quite common in multivariate analysis and widespread in a number of applications, the problem of testing the null hypothesis of ellipticity so far has not been addressed in a fully…

This paper studies optimal hypothesis testing for nonregular econometric models with parameter-dependent support. We consider both one-sided and two-sided hypothesis testing and develop asymptotically uniformly most powerful tests based on…

We consider sequential hypothesis testing based on observations which are received in groups of random size. The observations are assumed to be independent both within and between the groups. We assume that the group sizes are independent…

We provide asymptotic results and develop high frequency statistical procedures for time-changed L\'evy processes sampled at random instants. The sampling times are given by first hitting times of symmetric barriers whose distance with…

We compute the exact asymptotics for the cumulants of linear statistics associated with the zeros counting measure of a large class of real Gaussian processes. Precisely, we show that if the underlying covariance function is regular and…

This paper presents a general asymptotic theory of sequential Bayesian estimation giving results for the strongest, almost sure convergence. We show that under certain smoothness conditions on the probability model, the greedy information…

This paper introduces a quasi-likelihood ratio testing procedure for diffusion processes observed under nonsynchronous sampling schemes. High-frequency data, particularly in financial econometrics, are often recorded at irregular time…

In this paper, we study the asymptotic relation between the maximum of acontinuous order statistics process formed by stationary Gaussian processesand the maximum of this process sampled at discrete time points. It is shown that, these two…

In this paper we present some new limit theorems for power variation of $k$th order increments of stationary increments L\'evy driven moving averages. In the infill asymptotic setting, where the sampling frequency converges to zero while…

Automatic evaluation with large language models, commonly known as LLM-as-a-judge, is now standard across reasoning and alignment tasks. Despite evaluating many samples in deployment, these evaluators typically (i) treat each case…

In this paper, we study the optimal multiple stopping problem under the filtration consistent nonlinear expectations. The reward is given by a set of random variables satisfying some appropriate assumptions rather than an RCLL process. We…

We determine the asymptotic behavior of the realized power variations, or more generally of sums of a given test function evaluated at the successive increments of a L\'{e}vy process. One can completely elucidate the first order behavior…

Efficient estimation of a non-Gaussian stable Levy process with drift and symmetric jumps observed at high frequency is considered. For this statistical experiment, the local asymptotic normality of the likelihood is proved with a…

Ordered testing procedures are multiple testing procedures that exploit a pre-specified ordering of the null hypotheses, from most to least promising. We analyze and compare the power of several recent proposals using the asymptotic…

Confidence sequences, anytime p-values (called p-processes in this paper), and e-processes all enable sequential inference for composite and nonparametric classes of distributions at arbitrary stopping times. Examining the literature, one…