Related papers: Confidence regions for the multinomial parameter w…
We propose a way to construct fiducial distributions for a multidimensional parameter using a step-by-step conditional procedure related to the inferential importance of the components of the parameter. For discrete models, in which the…
In this paper, we use the empirical likelihood method to construct the confidence regions for the difference between the parameters of a two-phases nonlinear model with random design. We show that the empirical likelihood ratio has an…
We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…
We explore a novel methodology for constructing confidence regions for parameters of linear models, using predictions from any arbitrary predictor. Our framework requires minimal assumptions on the noise and can be extended to functions…
Solutions to inverse problems that are ill-conditioned or ill-posed may have significant intrinsic uncertainty. Unfortunately, analysing and quantifying this uncertainty is very challenging, particularly in high-dimensional problems. As a…
Precision matrices play important roles in many practical applications. Motivated by temporally dependent multivariate data in modern social and scientific studies, we consider the statistical inference of precision matrices for…
It is well known that the empirical likelihood ratio confidence region suffers finite sample under-coverage issue, and this severely hampers its application in statistical inferences.} The root cause of this under-coverage is an upper limit…
Estimating the parameters from $k$ independent Bin$(n,p)$ random variables, when both parameters $n$ and $p$ are unknown, is relevant to a variety of applications. It is particularly difficult if $n$ is large and $p$ is small. Over the past…
Statistical inference in high-dimensional settings is challenging when standard unregularized methods are employed. In this work, we focus on the case of multiple correlated proportions for which we develop a Bayesian inference framework.…
Estimating high quantiles plays an important role in the context of risk management. This involves extrapolation of an unknown distribution function. In this paper we propose three methods, namely, the normal approximation method, the…
We consider the problem of constructing honest and adaptive confidence sets in Lp-loss (with p>=1 and p < infinity) over sets of Sobolev-type classes, in the setting of non-parametric Gaussian regression. The objective is to adapt the…
Classical asymptotic theory for statistical inference usually involves calibrating a statistic by fixing the dimension $d$ while letting the sample size $n$ increase to infinity. Recently, much effort has been dedicated towards…
We derive the asymptotic distribution of the domination number of a new family of random digraph called proximity catch digraph (PCD), which has application to statistical testing of spatial point patterns and to pattern recognition. The…
Conformal methods create prediction bands that control average coverage under no assumptions besides i.i.d. data. Besides average coverage, one might also desire to control conditional coverage, that is, coverage for every new testing…
Confidence sequences are collections of confidence regions that simultaneously cover the true parameter for every sample size at a prescribed confidence level. Tightening these sequences is of practical interest and can be achieved by…
Conformal prediction builds marginally valid prediction intervals that cover the unknown outcome of a randomly drawn test point with a prescribed probability. However, in practice, data-driven methods are often used to identify specific…
Existing inferential methods for small area data involve a trade-off between maintaining area-level frequentist coverage rates and improving inferential precision via the incorporation of indirect information. In this article, we propose a…
Practical or scientific considerations often lead to selecting a subset of parameters as ``important.'' Inferences about those parameters often are based on the same data used to select them in the first place. That can make the reported…
It is well known that if the power spectral density of a continuous time stationary stochastic process does not have a compact support, data sampled from that process at any uniform sampling rate leads to biased and inconsistent spectrum…
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.…