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Conditional independence (CI) is central to causal inference, feature selection, and graphical modeling, yet it is untestable in many settings without additional assumptions. Existing CI tests often rely on restrictive structural…
We discuss tests of the Einstein Equivalence Principle due to energies which are purely quantum mechanical in origin. In particular, we consider using Lamb Shift energies to test for possible quantum violations of Local Position Invariance.…
We investigate the behavior of the Generalized Likelihood Ratio Test (GLRT) (Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193]) for time varying coefficient models where the regressors and errors are non-stationary time series and can…
Conditional independence (CI) testing is a fundamental and challenging task in modern statistics and machine learning. Many modern methods for CI testing rely on powerful supervised learning methods to learn regression functions or Bayes…
We consider the problem of testing for long-range dependence in time-varying coefficient regression models, where the covariates and errors are locally stationary, allowing complex temporal dynamics and heteroscedasticity. We develop KPSS,…
A strictly stationary sequence of random variables is constructed with the following properties: (i) the random variables take the values -1 and +1 with probability 1/2 each, (ii) every five of the random variables are independent, (iii)…
We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…
Testing for stability in linear panel data models has become an important topic in both the statistics and econometrics research communities. The available methodologies address testing for changes in the mean/linear trend, or testing for…
Simulation-based inference plays a major role in modern statistics, and often employs either reallocating (as in a randomization test) or resampling (as in bootstrapping). Reallocating mimics random allocation to treatment groups, while…
When conducting a Bell test, it is normal to assume that the preparation of the quantum state is independent of the measurements performed on it. Remarkably, the violation of local realism by entangled quantum systems can be certified even…
We develop a fully non-parametric, easy-to-use, and powerful test for the missing completely at random (MCAR) assumption on the missingness mechanism of a dataset. The test compares distributions of different missing patterns on random…
We consider the problem of testing whether a single coefficient is equal to zero in linear models when the dimension of covariates $p$ can be up to a constant fraction of sample size $n$. In this regime, an important topic is to propose…
Randomization testing is a fundamental method in statistics, enabling inferential tasks such as testing for (conditional) independence of random variables, constructing confidence intervals in semiparametric location models, and…
In this paper, we develop invariance-based procedures for testing and inference in high-dimensional regression models. These procedures, also known as randomization tests, provide several important advantages. First, for the global null…
Model-X approaches to testing conditional independence between a predictor and an outcome variable given a vector of covariates usually assume exact knowledge of the conditional distribution of the predictor given the covariates.…
We investigate the performance of large language models on repetitive deterministic prediction tasks and study how the sequence accuracy rate scales with output length. Each such task involves repeating the same operation n times. Examples…
We propose a novel algorithm for testing the hypothesis of nonstationarity in complex-valued signals. The implementation uses both the bootstrap and the Fast Fourier Transform such that the algorithm can be efficiently implemented in…
The paper introduces robust independence tests with non-asymptotically guaranteed significance levels for stochastic linear time-invariant systems, assuming that the observed outputs are synchronous, which means that the systems are driven…
One central goal of design of observational studies is to embed non-experimental data into an approximate randomized controlled trial using statistical matching. Despite empirical researchers' best intention and effort to create…
Mendelian randomization (MR) has been a popular method in genetic epidemiology to estimate the effect of an exposure on an outcome using genetic variants as instrumental variables (IV), with two-sample summary-data MR being the most…