Related papers: Finite Sample Inference in Incomplete Models

Experimental designs based on the classical D-optimal criterion minimize the volume of the linear-approximation inference regions for the parameters using local sensitivity coefficients. For nonlinear models, these designs can be unreliable…

In multivariate nonparametric regression the additive models are very useful when a suitable parametric model is difficult to find. The backfitting algorithm is a powerful tool to estimate the additive components. However, due to complexity…

A framework is presented for fitting inverse problem models via variational Bayes approximations. This methodology guarantees flexibility to statistical model specification for a broad range of applications, good accuracy and reduced model…

We show that confidence intervals in a variance component model, with asymptotically correct uniform coverage probability, can be obtained by inverting certain test-statistics based on the score for the restricted likelihood. The results…

We study the Inexact Restoration framework with random models for minimizing functions whose evaluation is subject to errors. We propose a constrained formulation that includes well-known stochastic problems and an algorithm applicable when…

We develop a theoretical framework for studying numerical estimation of lower previsions, generally applicable to two-level Monte Carlo methods, importance sampling methods, and a wide range of other sampling methods one might devise. We…

Consider a problem of predicting a response variable using a set of covariates in a linear regression model. If it is \emph{a priori} known or suspected that a subset of the covariates do not significantly contribute to the overall fit of…

This paper proposes new specification tests for conditional models with discrete responses, which are key to apply efficient maximum likelihood methods, to obtain consistent estimates of partial effects and to get appropriate predictions of…

The deployment of safe and trustworthy machine learning systems, and particularly complex black box neural networks, in real-world applications requires reliable and certified guarantees on their performance. The conformal prediction…

When causal quantities cannot be point identified, researchers often pursue partial identification to quantify the range of possible values. However, the peculiarities of applied research conditions can make this analytically intractable.…

Constraints can be interpreted in a broad sense as any kind of explicit restriction over the parameters. While some constraints are defined directly on the parameter space, when they are instead defined by known behaviour on the model,…

Extending to dimension 2 and higher the dual univariate concepts of ranks and quantiles has remained an open problem for more than half a century. Based on measure transportation results, a solution has been proposed recently under the name…

This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple…

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…

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…

Stationary points or derivative zero crossings of a regression function correspond to points where a trend reverses, making their estimation scientifically important. Existing approaches to uncertainty quantification for stationary points…

We present a method for computing A-optimal sensor placements for infinite-dimensional Bayesian linear inverse problems governed by PDEs with irreducible model uncertainties. Here, irreducible uncertainties refers to uncertainties in the…

Hypothesis testing procedures are developed to assess linear operator constraints in function-on-scalar regression when incomplete functional responses are observed. The approach enables statistical inferences about the shape and other…

We consider optimal design of infinite-dimensional Bayesian linear inverse problems governed by partial differential equations that contain secondary reducible model uncertainties, in addition to the uncertainty in the inversion parameters.…

Conformal prediction provides a distribution-free framework for uncertainty quantification via prediction sets with exact finite-sample coverage. In low dimensions these sets are easy to interpret, but in high-dimensional or structured…