Related papers: Optimum Statistical Test Procedure
The ``fast iterative shrinkage-thresholding algorithm'', a.k.a. FISTA, is one of the most widely used algorithms in the literature. However, despite its optimal theoretical $O(1/k^2)$ convergence rate guarantee, oftentimes in practice its…
This paper aims to motivate stochastic optimization problems from a statistical perspective and a statistical learning perspective, where the goal is to maximize the log-likelihood or minimize the population risk. We briefly describe the…
We present a new algorithm to optimize distributions defined implicitly by parameterized stochastic diffusions. Doing so allows us to modify the outcome distribution of sampling processes by optimizing over their parameters. We introduce a…
Group testing is an efficient method for testing a large population to detect infected individuals. In this paper, we consider an efficient adaptive two stage group testing scheme. Using a straightforward analysis, we characterize the…
This paper presents a formal framework for identifying and filtering SPIT calls (SPam in Internet Telephony) in an outbound scenario with provable optimal performance. In so doing, our work is largely different from related previous work:…
In this paper, we develop an approach for the exact determination of the minimum sample size for the estimation of a Poisson parameter with prescribed margin of error and confidence level. The exact computation is made possible by reducing…
Measurements are generally collected as unilateral or bilateral data in clinical trials or observational studies. For example, in ophthalmologic studies, statistical tests are often based on one or two eyes of an individual. For bilateral…
We introduce random matrix theory to study the tomographic efficiency of a wide class of measurements constructed out of weighted 2-designs, including symmetric informationally complete (SIC) probability operator measurements (POMs). In…
To fast approximate maximum likelihood estimators with massive data, this paper studies the Optimal Subsampling Method under the A-optimality Criterion (OSMAC) for generalized linear models. The consistency and asymptotic normality of the…
In diagnostic testing, establishing an indeterminate class is an effective way to identify samples that cannot be accurately classified. However, such approaches also make testing less efficient and must be balanced against overall assay…
This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…
We address the following state comparison problem: is it possible to design an experiment enabling us to unambiguously decide (based on the observed outcome statistics) on the sameness or difference of two unknown state preparations without…
A signal recovery problem is considered, where the same binary testing problem is posed over multiple, independent data streams. The goal is to identify all signals, i.e., streams where the alternative hypothesis is correct, and noises,…
To identify statistically significant conclusions, it is proposed to simultaneously test hypotheses and alternatives. It is shown that, under the condition of free combination of hypotheses and alternatives, the closure method leads to…
In this note, we present a novel measure of similarity between two functions. It quantifies how the sub-optimality gaps of two functions convert to each other, and unifies several existing notions of functional similarity. We show that it…
We study the robust quickest change detection under unknown pre- and post-change distributions. To deal with uncertainties in the data-generating distributions, we formulate two data-driven ambiguity sets based on the Wasserstein distance,…
We propose new, optimal methods for analyzing randomized trials, when it is suspected that treatment effects may differ in two predefined subpopulations. Such sub-populations could be defined by a biomarker or risk factor measured at…
In this paper a new solution is proposed for testing simple stwo stage electronic circuits. It minimizes the number of tests to be performed to determine the genuinity of the circuit. The main idea behind the present research work is to…
The use of group testing to locate all instances of disease in a large population of blood samples was first considered seventy years ago. Since then, several methods have been used to approximate the minimum expected number of tests. The…
We undertake a critical evaluation of recent observational information on $\Omega_m$ and $\Omega_\Lambda$ in order to identify possible sources of systematic errors and effects of simplified statistical analyses. We combine observations for…