Related papers: Non-asymptotic theory for nonparametric testing

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 this paper, we introduce a targeted exploration strategy for the non-asymptotic, finite-time case. The proposed strategy is applicable to uncertain linear time-invariant systems subject to sub-Gaussian disturbances. As the main result,…

We investigate and compare the fundamental performance of several distributed learning methods that have been proposed recently. We do this in the context of a distributed version of the classical signal-in-Gaussian-white-noise model, which…

We study sequential multiple testing with independent data streams, where the goal is to identify an unknown subset of signals while controlling commonly used error metrics, including generalized familywise rates and false discovery and…

In the asymptotic theory of quantum hypothesis testing, the minimal error probability of the first kind jumps sharply from zero to one when the error exponent of the second kind passes by the point of the relative entropy of the two states…

We propose to address the common problem of linear estimation in linear statistical models by using a model selection approach via penalization. Depending then on the framework in which the linear statistical model is considered namely the…

Flexible estimation of the mean outcome under a treatment regimen (i.e., value function) is the key step toward personalized medicine. We define our target parameter as a conditional value function given a set of baseline covariates which…

Along the lines of Janssen's and Pfanzagl's work the testing theory for statistical functionals is further developed for non-parametric one-sample problems. Efficient tests for the one-sided and two-sided problems are derived for…

Nonparametric two sample testing deals with the question of consistently deciding if two distributions are different, given samples from both, without making any parametric assumptions about the form of the distributions. The current…

Asymptotic optimality is a key theoretical property in model averaging. Due to technical difficulties, existing studies rely on restricted weight sets or the assumption that there is no true model with fixed dimensions in the candidate set.…

We propose a nonparametric procedure to test for changes in correlation matrices at an unknown point in time. The new test requires only mild assumptions on the serial dependence structure and has considerable power in finite samples. We…

Measurements of quantum states form a key component in quantum-information processing. It is therefore an important task to compare measurements and furthermore decide if a measurement strategy is optimal. Entropic quantities, such as the…

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…

We propose a methodology for testing linear hypothesis in high-dimensional linear models. The proposed test does not impose any restriction on the size of the model, i.e. model sparsity or the loading vector representing the hypothesis.…

This paper considers the asymptotic theory of a semiparametric M-estimator that is generally applicable to models that satisfy a monotonicity condition in one or several parametric indexes. We call the estimator two-stage maximum score…

Within the nonparametric regression model with unknown regression function $l$ and independent, symmetric errors, a new multiscale signed rank statistic is introduced and a conditional multiple test of the simple hypothesis $l=0$ against a…

We study the problems of sequential nonparametric two-sample and independence testing. Sequential tests process data online and allow using observed data to decide whether to stop and reject the null hypothesis or to collect more data,…

In this paper, in order to test whether changes have occurred in a nonlinear parametric regression, we propose a nonparametric method based on the empirical likelihood. Firstly, we test the null hypothesis of no-change against the…

We formulate nonparametric and semiparametric hypothesis testing of multivariate stationary linear time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix. The limiting…

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…