相关论文: The Cost of Sequential Adaptation and the Lower Bo…

In this work the primary objective is to maximize the precision of the maximum likelihood estimate in a linear regression model through the efficient design of the experiment. One common measure of precision is the unconditional mean square…

Most studies of adaptive algorithm behavior consider performance measures based on mean values such as the mean-square error. The derived models are useful for understanding the algorithm behavior under different environments and can be…

Adaptive designs have been proposed for clinical trials in which the nuisance parameters or alternative of interest are unknown or likely to be misspecified before the trial. Whereas most previous works on adaptive designs and mid-course…

A two-stage adaptive optimal design is an attractive option for increasing the efficiency of clinical trials. In these designs, based on interim data, the locally optimal dose is chosen for further exploration, which induces dependencies…

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…

The Fisher information approximation (FIA) is an implementation of the minimum description length principle for model selection. Unlike information criteria such as AIC or BIC, it has the advantage of taking the functional form of a model…

We prove two lower bounds for the complexity of non-log-concave sampling within the framework of Balasubramanian et al. (2022), who introduced the use of Fisher information (FI) bounds as a notion of approximate first-order stationarity in…

We consider the problem of sequential sampling from a finite number of independent statistical populations to maximize the expected infinite horizon average outcome per period, under a constraint that the expected average sampling cost does…

We prove lower bounds on the error of any estimator for the mean of a real probability distribution under the knowledge that the distribution belongs to a given set. We apply these lower bounds both to parametric and nonparametric…

This paper provides a systematic approach to semiparametric identification that is based on statistical information as a measure of its "quality". Identification can be regular or irregular, depending on whether the Fisher information for…

This paper studies transfer learning for estimating the mean of random functions based on discretely sampled data, where, in addition to observations from the target distribution, auxiliary samples from similar but distinct source…

Adapting the final sample size of a trial to the evidence accruing during the trial is a natural way to address planning uncertainty. Designs with adaptive sample size need to account for their optional stopping to guarantee strict type-I…

It is generally appreciated that a frequentist analysis of a group sequential trial must in order to avoid inflating type I error account for the fact that one or more interim analyses were performed. It is also to a lesser extent realised…

This paper considers least-square based estimation of the amplitude and square amplitude of a quantized sine wave, done by considering random initial record phase. Using amplitude- and frequency-domain modeling techniques, it is shown that…

State estimation that combines observational data with mathematical models is central to many applications and is commonly addressed through filtering methods, such as ensemble Kalman filters. In this article, we examine the signal-tracking…

I present several new relations between mutual information (MI) and statistical estimation error for a system that can be regarded simultaneously as a communication channel and as an estimator of an input parameter. I first derive a…

This paper studies empirical risk minimization (ERM) problems for large-scale datasets and incorporates the idea of adaptive sample size methods to improve the guaranteed convergence bounds for first-order stochastic and deterministic…

Researchers may perform regressions using a sketch of data of size $m$ instead of the full sample of size $n$ for a variety of reasons. This paper considers the case when the regression errors do not have constant variance and…

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…

Stochastic models that predict adaptive filtering algorithms performance usually employ several assumptions in order to simplify the analysis. Although these simplifications facilitate the recursive update of the statistical quantities of…