Related papers: On the Precise Asymptotics of Universal Inference
Uniformly valid inference for cointegrated vector autoregressive processes has so far proven difficult due to certain discontinuities arising in the asymptotic distribution of the least squares estimator. We extend asymptotic results from…
The current standard for confidence interval construction in the context of a possibly misspecified model is to use an interval based on the sandwich estimate of variance. These intervals provide asymptotically correct coverage, but…
We present an informal review of recent work on the asymptotics of Approximate Bayesian Computation (ABC). In particular we focus on how does the ABC posterior, or point estimates obtained by ABC, behave in the limit as we have more data?…
Inverse Probability Weighting (IPW) is widely used in empirical work in economics and other disciplines. As Gaussian approximations perform poorly in the presence of "small denominators," trimming is routinely employed as a regularization…
This paper provides a set of methods for quantifying the robustness of treatment effects estimated using the unconfoundedness assumption (also known as selection on observables or conditional independence). Specifically, we estimate and do…
For a partial structural change in a linear regression model with a single break, we develop a continuous record asymptotic framework to build inference methods for the break date. We have T observations with a sampling frequency h over a…
Using and extending fractional order statistic theory, we characterize the $O(n^{-1})$ coverage probability error of the previously proposed confidence intervals for population quantiles using $L$-statistics as endpoints in Hutson (1999).…
In this paper, we study frequentist coverage errors of Bayesian credible sets for an approximately linear regression model with (moderately) high dimensional regressors, where the dimension of the regressors may increase with but is smaller…
We develop a collection of methods for adjusting the predictions of quantile regression to ensure coverage. Our methods are model agnostic and can be used to correct for high-dimensional overfitting bias with only minimal assumptions.…
We generalize standard credal set models for imprecise probabilities to include higher order credal sets -- confidences about confidences. In doing so, we specify how an agent's higher order confidences (credal sets) update upon observing…
A long-standing problem in the construction of asymptotically correct confidence bands for a regression function $m(x)=E[Y|X=x]$, where $Y$ is the response variable influenced by the covariate $X$, involves the situation where $Y$ values…
Belief tracking is a basic problem in planning with sensing. While the problem is intractable, it has been recently shown that for both deterministic and non-deterministic systems expressed in compact form, it can be done in time and space…
Estimating the data uncertainty in regression tasks is often done by learning a quantile function or a prediction interval of the true label conditioned on the input. It is frequently observed that quantile regression -- a vanilla algorithm…
Credal sets, i.e., closed convex sets of probability measures, provide a natural framework to represent aleatoric and epistemic uncertainty in machine learning. Yet how to quantify these two types of uncertainty for a given credal set,…
When studying the causal effect of $x$ on $y$, researchers may conduct regression and report a confidence interval for the slope coefficient $\beta_{x}$. This common confidence interval provides an assessment of uncertainty from sampling…
Prediction sets provide a means of quantifying the uncertainty in predictive tasks. Using held out calibration data, conformal prediction and risk control can produce prediction sets that exhibit statistically valid error control in a…
Nonparametric methods play a central role in modern empirical work. While they provide inference procedures that are more robust to parametric misspecification bias, they may be quite sensitive to tuning parameter choices. We study the…
In modern data analysis, it is common to select a model before performing statistical inference. Selective inference tools make adjustments for the model selection process in order to ensure reliable inference post selection. In this paper,…
We consider the adaptive Lasso estimator with componentwise tuning in the framework of a low-dimensional linear regression model. In our setting, at least one of the components is penalized at the rate of consistent model selection and…
The goal of this paper is to give confidence regions for the excursion set of a spatial function above a given threshold from repeated noisy observations on a fine grid of fixed locations. Given an asymptotically Gaussian estimator of the…