Related papers: Valid confidence intervals for regression with bes…

Adaptive confidence intervals for regression functions are constructed under shape constraints of monotonicity and convexity. A natural benchmark is established for the minimum expected length of confidence intervals at a given function in…

Aim: The Akaike information Criterion (AIC) is widely used science to make predictions about complex phenomena based on an entire set of models weighted by Akaike weights. This approach (AIC model averaging; hereafter AvgAICc) is often…

Consider the spiked Wigner model \[ X = \sum_{i = 1}^k \lambda_i u_i u_i^\top + \sigma G, \] where $G$ is an $N \times N$ GOE random matrix, and the eigenvalues $\lambda_i$ are all spiked, i.e. above the Baik-Ben Arous-P\'ech\'e (BBP)…

Accurate conditional prediction in the regression setting plays an important role in many real-world problems. Typically, a point prediction often falls short since no attempt is made to quantify the prediction accuracy. Classically, under…

We address the challenge of constructing valid confidence intervals and sets in problems of prediction across multiple environments. We investigate two types of coverage suitable for these problems, extending the jackknife and…

A stochastic search method, the so-called Adaptive Subspace (AdaSub) method, is proposed for variable selection in high-dimensional linear regression models. The method aims at finding the best model with respect to a certain model…

Random effects meta-analysis is a widely applied methodology to synthetize research findings of studies in a specific scientific question. Besides estimating the mean effect, an important aim of the meta-analysis is to summarize the…

We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the number of potentially important…

Selective classification, in which models can abstain on uncertain predictions, is a natural approach to improving accuracy in settings where errors are costly but abstentions are manageable. In this paper, we find that while selective…

This paper considers the problem of approximating a density when it can be evaluated up to a normalizing constant at a limited number of points. We call this problem the Boltzmann approximation (BA) problem. The BA problem is ubiquitous in…

Model selection is the problem of distinguishing competing models, perhaps featuring different numbers of parameters. The statistics literature contains two distinct sets of tools, those based on information theory such as the Akaike…

Methods for combining predictions from different models in a supervised learning setting must somehow estimate/predict the quality of a model's predictions at unknown future inputs. Many of these methods (often implicitly) make the…

By generating prediction intervals (PIs) to quantify the uncertainty of each prediction in deep learning regression, the risk of wrong predictions can be effectively controlled. High-quality PIs need to be as narrow as possible, whilst…

Error propagation formulae are derived for the expectation-maximization iterative unfolding algorithm regularized by a smoothing step. The effective number of parameters in the fit to the observed data is defined for unfolding procedures.…

In this article, we review selective inference, a set of techniques for inference when the statistical question asked is a function of the data. This setting often arises in contemporary scientific workflows, where hypotheses and parameters…

In a supervised online setting, quantifying uncertainty has been proposed in the seminal work of \cite{gibbs2021adaptive}. For any given point-prediction algorithm, their method (ACI) produces a conformal prediction set with an average…

We propose information criteria that measure the prediction risk of a predictive density based on the Bayesian marginal likelihood from a frequentist point of view. We derive criteria for selecting variables in linear regression models,…

Smoothed AIC (S-AIC) and Smoothed BIC (S-BIC) are very widely used in model averaging and are very easily to implement. Especially, the optimal model averaging method MMA and JMA have only been well developed in linear models. Only by…

Boosting methods are widely used in statistical learning to deal with high-dimensional data due to their variable selection feature. However, those methods lack straightforward ways to construct estimators for the precision of the…

This paper compares three approaches to the problem of selecting among probability models to fit data (1) use of statistical criteria such as Akaike's information criterion and Schwarz's "Bayesian information criterion," (2) maximization of…