Related papers: Catoni-style Confidence Sequences under Infinite V…
For time series with high temporal correlation, the empirical process converges rather slowly to its limiting distribution. Many statistics in change-point analysis, goodness-of-fit testing and uncertainty quantification admit a…
Valid inference after model selection is currently a very active area of research. The polyhedral method, pioneered by Lee, et al. (2016), allows for valid inference after model selection if the model selection event can be described by…
This paper studies the propagation of finite-sample uncertainty under nonlinear transformations commonly used in statistical decision systems. In particular, we consider process capability indices, which are widely used in manufacturing…
The beta family owes its privileged status within unit interval distributions to several relevant features such as, for example, easyness of interpretation and versatility in modeling different types of data. However, its flexibility at the…
This paper studies higher-order inference properties of nonparametric local polynomial regression methods under random sampling. We prove Edgeworth expansions for $t$ statistics and coverage error expansions for interval estimators that (i)…
We compute bias, variance, and approximate confidence intervals for the efficiency of a random selection process under various special conditions that occur in practical data analysis. We consider the following cases: a) the number of…
Confidence intervals based on the central limit theorem (CLT) are a cornerstone of classical statistics. Despite being only asymptotically valid, they are ubiquitous because they permit statistical inference under weak assumptions and can…
Conformal prediction is an assumption-lean approach to generating distribution-free prediction intervals or sets, for nearly arbitrary predictive models, with guaranteed finite-sample coverage. Conformal methods are an active research topic…
We recall some of the history of the information-theoretic approach to deriving core results in probability theory and indicate parts of the recent resurgence of interest in this area with current progress along several interesting…
Transductive conformal prediction addresses the simultaneous prediction for multiple data points. Given a desired confidence level, the objective is to construct a prediction set that includes the true outcomes with the prescribed…
We extend in two directions our previous results about the sampling and the empirical measures of immortal branching Markov processes. Direct applications to molecular biology are rigorous estimates of the mutation rates of polymerase chain…
We focus on the problem estimating a monotone trend function under additive and dependent noise. New point-wise confidence interval estimators under both short- and long-range dependent errors are introduced and studied. These intervals are…
Parameters of sub-populations can be more relevant than super-population ones. For example, a healthcare provider may be interested in the effect of a treatment plan for a specific subset of their patients; policymakers may be concerned…
This paper extends standard results from learning theory with independent data to sequences of dependent data. Contrary to most of the literature, we do not rely on mixing arguments or sequential measures of complexity and derive uniform…
We consider estimating the shared mean of a sequence of heavy-tailed random variables taking values in a Banach space. In particular, we revisit and extend a simple truncation-based mean estimator first proposed by Catoni and Giulini. While…
Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with…
In scientific disciplines such as neuroimaging, climatology, and cosmology it is useful to study the uncertainty of excursion sets of imaging data. While the case of imaging data obtained from a single study condition has already been…
Diffusion model-based approaches have shown promise in data-driven planning, but there are no safety guarantees, thus making it hard to be applied for safety-critical applications. To address these challenges, we propose a new method,…
The results of difference sequences theory are applied to analytic function theory and Diophantine equations. As a result we have the equation which connects the $n$-th derivative of a function with the difference sequence for the values of…
An implicit finite difference method with non-uniform timesteps for solving the fractional diffusion equation in the Caputo form is proposed. The method allows one to build adaptive methods where the size of the timesteps is adjusted to the…