Related papers: Asymptotic Representations for Sequential Decision…
Non-standard distributional approximations have received considerable attention in recent years. They often provide more accurate approximations in small samples, and theoretical improvements in some cases. This paper shows that the…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
In modern data analysis, it is common to select a model before performing statistical inference. Selective inference tools make adjustments for the model selection process in order to ensure reliable inference post selection. In this paper,…
Recently, it has been shown how sampling actions from the predictive distribution over the optimal action-sometimes called Thompson sampling-can be applied to solve sequential adaptive control problems, when the optimal policy is known for…
This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for…
Adaptive experiments such as multi-arm bandits adapt the treatment-allocation policy and/or the decision to stop the experiment to the data observed so far. This has the potential to improve outcomes for study participants within the…
Recent years have seen tremendous advances in the theory and application of sequential experiments. While these experiments are not always designed with hypothesis testing in mind, researchers may still be interested in performing tests…
In time series analysis, statistics based on collections of estimators computed from sub-samples play a crucial role in an increasing variety of important applications. Proving results about the joint asymptotic distribution of such…
In this monograph, we prove an asymptotic approximation for integrals of probability densities over sets in finite dimensional euclidean space, which are far away from the origin (asymptotic sets). We use this approximation to investigate…
We study asymptotic behavior of one-step weighted $M$-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent weighted…
We consider an experiment with at least two stages or batches and $O(N)$ subjects per batch. First, we propose a semiparametric treatment effect estimator that efficiently pools information across the batches, and show it asymptotically…
In this paper, we consider asymptotics of the optimal value and the optimal solutions of parametric minimax estimation problems. Specifically, we consider estimators of the optimal value and the optimal solutions in a sample minimax problem…
Adaptive experiments are used extensively in online platforms, healthcare and biotechnology, and a variety of other settings. In many of these applications, the main goal is not to precisely estimate a treatment effect, but to demonstrate…
In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points.…
We consider parametric estimation and tests for multi-dimensional diffusion processes with a small dispersion parameter $\varepsilon$ from discrete observations. For parametric estimation of diffusion processes, the main target is to…
We consider the problem of efficient inference of the Average Treatment Effect in a sequential experiment where the policy governing the assignment of subjects to treatment or control can change over time. We first provide a central limit…
We consider sequential hypothesis testing between two quantum states using adaptive and non-adaptive strategies. In this setting, samples of an unknown state are requested sequentially and a decision to either continue or to accept one of…
Multi-arm bandit experimental designs are increasingly being adopted over standard randomized trials due to their potential to improve outcomes for study participants, enable faster identification of the best-performing options, and/or…
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…
In this note, we are concerned with the asymptotic approximation of a class of double integrals which can be represented as an angular spectrum superposition. These double integrals typically appear in electromagnetic scattering problems.…