Related papers: Confidence Intervals from One One Observation
In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random…
Statistical inference of the high-dimensional regression coefficients is challenging because the uncertainty introduced by the model selection procedure is hard to account for. A critical question remains unsettled; that is, is it possible…
Based on a progressively type-II censored sample from the exponential distribution with unknown location and scale parameter, confidence bands are proposed for the underlying distribution function by using confidence regions for the…
If nonlocality is to be inferred from a violation of Bell's inequality, an important assumption is that the measurement settings are freely chosen by the observers, or alternatively, that they are random and uncorrelated with the…
We propose a multi-scale extension of conformal prediction, an approach that constructs prediction sets with finite-sample coverage guarantees under minimal statistical assumptions. Classic conformal prediction relies on a single notion of…
Sensors are the key to environmental monitoring, which impart benefits to smart cities in many aspects, such as providing real-time air quality information to assist human decision-making. However, it is impractical to deploy massive…
Newton-step approximations to pseudo maximum likelihood estimates of spatial autoregressive models with a large number of parameters are examined, in the sense that the parameter space grows slowly as a function of sample size. These have…
A calculator program has been written to give confidence intervals on branching ratios for rare decay modes (or similar quantities) calculated from the number of events observed, the acceptance factor, the background estimate and the…
We consider the problem of estimating the support of a measure from a finite, independent, sample. The estimators which are considered are constructed based on the empirical Christoffel function. Such estimators have been proposed for the…
Applied macroeconomists often compute confidence intervals for impulse responses using local projections, i.e., direct linear regressions of future outcomes on current covariates. This paper proves that local projection inference robustly…
For statistical inference on an infinite-dimensional Hilbert space $\H $ with no moment conditions we introduce a new class of energy distances on the space of probability measures on $\H$. The proposed distances consist of the integrated…
A rich set of frequentist model averaging methods has been developed, but their applications have largely been limited to point prediction, as measuring prediction uncertainty in general settings remains an open problem. In this paper we…
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…
In this paper we offer a unified approach to the problem of nonparametric regression on the unit interval. It is based on a universal, honest and non-asymptotic confidence region which is defined by a set of linear inequalities involving…
We consider the problem of constructing pointwise confidence intervals in the multiple isotonic regression model. Recently, [HZ19] obtained a pointwise limit distribution theory for the so-called block max-min and min-max estimators [FLN17]…
We present a new method for constructing a confidence interval for the mean of a bounded random variable from samples of the random variable. We conjecture that the confidence interval has guaranteed coverage, i.e., that it contains the…
The inability of Machine Learning (ML) models to successfully extrapolate correct predictions from out-of-distribution (OoD) samples is a major hindrance to the application of ML in critical applications. Until the generalization ability of…
Existing concentration bounds for bounded vector-valued random variables include extensions of the scalar Hoeffding and Bernstein inequalities. While the latter is typically tighter, it requires knowing a bound on the variance of the random…
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…
This work presents a novel simulation-based approach for constructing confidence regions in parametric models, which is particularly suited for generative models and situations where limited data and conventional asymptotic approximations…