Related papers: Generalized Fiducial Inference for Ultrahigh Dimen…
Fiducial inference, as generalized by Hannig et al. (2016), is applied to nonparametric g-modeling (Efron, 2016) in the discrete case. We propose a computationally efficient algorithm to sample from the fiducial distribution, and use the…
Reacting against the limitation of statistics to decision procedures, R. A. Fisher proposed for inductive reasoning the use of the fiducial distribution, a parameter-space distribution of epistemological probability transferred directly…
Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…
We propose a new inferential framework for constructing confidence regions and testing hypotheses in statistical models specified by a system of high dimensional estimating equations. We construct an influence function by projecting the…
Inferential models have recently gained in popularity for valid uncertainty quantification. In this paper, we investigate inferential models by exploring relationships between inferential models, fiducial inference, and confidence curves.…
Post-data statistical inference concerns making probability statements about model parameters conditional on observed data. When a priori knowledge about parameters is available, post-data inference can be conveniently made from Bayesian…
The concept of fiducial inference was introduced by R. A. Fisher in the 1930s to address the perceived limitations of Bayesian inference, particularly the need for subjective prior distributions in cases with limited prior information.…
The purpose of this paper is to propose methodologies for statistical inference of low-dimensional parameters with high-dimensional data. We focus on constructing confidence intervals for individual coefficients and linear combinations of…
Estimating the difference between two binomial proportions will be investigated, where Bayesian, frequentist and fiducial (BFF) methods will be considered. Three vague priors will be used, the Jeffreys prior, a divergence prior and the…
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…
This paper is concerned with estimation and inference for ultrahigh dimensional partially linear single-index models. The presence of high dimensional nuisance parameter and nuisance unknown function makes the estimation and inference…
Fisher's fiducial probability has recently received renewed attention under the name confidence. In this paper, we reformulate it within an extended-likelihood framework, a representation that helps to resolve many long-standing…
Graphical models have become a very popular tool for representing dependencies within a large set of variables and are key for representing causal structures. We provide results for uniform inference on high-dimensional graphical models…
We present a multi-fidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution. In the Bayesian inference setting, traditional…
In the past two decades, there has been a fast-growing literature on fiducial inference since it was first proposed by R. A. Fisher in the 1930s. However, most of the fiducial inference based methods and related approaches have been…
High-dimensional statistical inference with general estimating equations are challenging and remain less explored. In this paper, we study two problems in the area: confidence set estimation for multiple components of the model parameters,…
Conformal prediction (CP) was developed to provide finite-sample probabilistic prediction guarantees. While CP algorithms are a relatively general-purpose approach to uncertainty quantification, with finite-sample guarantees, they lack…
We propose a likelihood ratio based inferential framework for high dimensional semiparametric generalized linear models. This framework addresses a variety of challenging problems in high dimensional data analysis, including incomplete…
Statistical inference as a formal scientific method to covert experience to knowledge has proven to be elusively difficult. While frequentist and Bayesian methodologies have been accepted in the contemporary era as two dominant schools of…
Fisher's fiducial argument is widely viewed as a failed version of Neyman's theory of confidence limits. But Fisher's goal -- Bayesian-like probabilistic uncertainty quantification without priors -- was more ambitious than Neyman's, and…