Related papers: Uniformly valid confidence intervals post-model-se…

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…

Inference methods for computing confidence intervals in parametric settings usually rely on consistent estimators of the parameter of interest. However, it may be computationally and/or analytically burdensome to obtain such estimators in…

A reasonable confidence interval should have a confidence coefficient no less than the given nominal level and a small expected length to reliably and accurately estimate the parameter of interest, and the bootstrap interval is considered…

A fundamental class of inferential problems are those characterised by there having been a substantial degree of pre-data (or prior) belief that the value of a model parameter was equal or lay close to a specified value, which may, for…

In the current insurance literature, prediction of insurance claims in the regression problem is often performed with a statistical model. This model-based approach may potentially suffer from several drawbacks: (i) model misspecification,…

Complex survey data are usually collected following complex sampling designs. Accounting for the sampling design is essential to obtain unbiased estimates and valid inferences when analyzing complex survey data. The area under the receiver…

We derive inferential procedures for large sample sizes that remain valid under data-dependent significance levels (so-called "post-hoc valid inference"). Classical statistical tools require that the significance level -- the "type-I error"…

We study high-dimensional linear models with error-in-variables. Such models are motivated by various applications in econometrics, finance and genetics. These models are challenging because of the need to account for measurement errors to…

Autoregressive models are a class of time series models that are important in both applied and theoretical statistics. Typically, inferential devices such as confidence sets and hypothesis tests for time series models require nuanced…

Standard penalized methods of variable selection and parameter estimation rely on the magnitude of coefficient estimates to decide which variables to include in the final model. However, coefficient estimates are unreliable when the design…

Gaussian processes have become a promising tool for various safety-critical settings, since the posterior variance can be used to directly estimate the model error and quantify risk. However, state-of-the-art techniques for safety-critical…

We examine the problem of construction of confidence intervals within the basic single-parameter, single-iteration variation of the method of quasi-optimal weights. Two kinds of distortions of such intervals due to insufficiently large…

In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…

Recent advances in machine learning have significantly improved prediction accuracy in various applications. However, ensuring the calibration of probabilistic predictions remains a significant challenge. Despite efforts to enhance model…

Selective inference aims at providing valid inference after a data-driven selection of models or hypotheses. It is essential to avoid overconfident results and replicability issues. While significant advances have been made in this area for…

Used to estimate the risk of an estimator or to perform model selection, cross-validation is a widespread strategy because of its simplicity and its apparent universality. Many results exist on the model selection performances of…

Survey sampling is concerned with the estimation of finite population parameters. In practice, survey data suffer from item nonresponse, which is commonly handled through imputation, i.e., replacing missing values with predicted values. As…

We study confidence interval construction for linear regression under Huber's contamination model, where an unknown fraction of noise variables is arbitrarily corrupted. While robust point estimation in this setting is well understood,…

Here we present an expository, general analysis of valid post-selection or post-regularization inference about a low-dimensional target parameter, $\alpha$, in the presence of a very high-dimensional nuisance parameter, $\eta$, which is…

For sparse high-dimensional regression problems, Cox and Battey [1, 9] emphasised the need for confidence sets of models: an enumeration of those small sets of variables that fit the data equivalently well in a suitable statistical sense.…