Related papers: Anytime-valid sequential testing for elicitable fu…
We give a necessary and sufficient condition for non-local functionals on vector-valued Lebesgue spaces to be weakly sequentially lower semi-continuous. Here a non-local functional shall have the form of a double integral of a density which…
Financial statement auditing is conducted under a risk-based evidence approach to obtain reasonable assurance. In practice, auditors often perform additional sampling or related procedures when an initial sample does not provide a…
We consider the recursive estimation of a regression functional where the explanatory variables take values in some functional space. We prove the almost sure convergence of such estimates for dependent functional data. Also we derive the…
It has been recently shown that e-processes are sufficient for sequential testing in the following sense: every level-$\alpha$ sequential test can be obtained by thresholding an e-process at $1/\alpha$. However, in the above result, neither…
We present a new distribution-free conformal prediction algorithm for sequential data (e.g., time series), called the \textit{sequential predictive conformal inference} (\texttt{SPCI}). We specifically account for the nature that time…
Deciding termination is a fundamental problem in the analysis of probabilistic imperative programs. We consider the qualitative and quantitative probabilistic termination problems for an imperative programming model with discrete…
The problem of testing for the parametric form of the conditional variance is considered in a fully nonparametric regression model. A test statistic based on a weighted $L_2$-distance between the empirical characteristic functions of…
We introduce the anytime-valid (AV) logrank test, a version of the logrank test that provides type-I error guarantees under optional stopping and optional continuation. The test is sequential without the need to specify a maximum sample…
We present a general nonparametric approach for testing whether a statistical parameter defined through conditional distributions is constant across the conditioning variables. Such hypotheses arise naturally in problems such as assessing…
We propose a general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model. It can be easily adjusted for multiplicity taking…
In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
In the setup of i.i.d.~observations and a real valued differentiable functional~$T$, locally asymptotic upper bounds are derived for the power of one-sided tests (simple, versus large values of~$T$)and for the confidence probability of…
We study finite-sample inference for the trade-off function of two unknown probability distributions, the function that traces the optimal type I/type II error frontier in binary testing. Given samples from distributions $P$ and $Q$, we…
We propose and analyze nonparametric tests of the null hypothesis that a function belongs to a specified parametric family. The tests are based on BIC approximations, \pi_{BIC}, to the posterior probability of the null model, and may be…
Given a strictly positive measure, we characterize inner semicontinuous solid convex-valued mappings for which continuous functions which are selections almost everywhere are selections. This class contains continuous mappings as well as…
We give estimates for the convolution product of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power…
We consider tests of hypotheses when the parameters are not identifiable under the null in semiparametric models, where regularity conditions for profile likelihood theory fail. Exponential average tests based on integrated profile…
In statistics, forecast uncertainty is often quantified using a specified statistical model, though such approaches may be vulnerable to model misspecification, selection bias, and limited finite-sample validity. While bootstrapping can…
This paper provides tests for detecting sample selection in nonparametric conditional quantile functions. The first test is an omitted predictor test with the propensity score as the omitted variable. As with any omnibus test, in the case…