Related papers: Point forecasting and forecast evaluation with gen…
Probability forecasts of events are routinely used in climate predictions, in forecasting default probabilities on bank loans or in estimating the probability of a patient's positive response to treatment. Scoring rules have long been used…
The present study proposes incorporating non-parametric knowledge into the diffusion least-mean-squares algorithm in the framework of a maximum a posteriori (MAP) estimation. The proposed algorithm leads to a robust estimation of an unknown…
We consider the problem of estimating the joint distribution of $n$ independent random variables. Our approach is based on a family of candidate probabilities that we shall call a model and which is chosen to either contain the true…
Calibration ensures that probabilistic forecasts meaningfully capture uncertainty by requiring that predicted probabilities align with empirical frequencies. However, many existing calibration methods are specialized for post-hoc…
In the context of linear regression, we construct a data-driven convex loss function with respect to which empirical risk minimisation yields optimal asymptotic variance in the downstream estimation of the regression coefficients. At the…
This paper focuses on the problem of the estimation of the cumulative hazard function of a distribution on a general complete separable metric space when the data points are subject to censoring by an arbitrary adapted random set. A problem…
This paper generalises inference functions (Godambe, 1960) to distributional statistical models, in which each probability measure is represented by a distribution--kernel pair $(T_\theta, \varphi) \in \mathcal S'(\mathbb R) \times \mathcal…
Robust estimation under Huber's $\epsilon$-contamination model has become an important topic in statistics and theoretical computer science. Statistically optimal procedures such as Tukey's median and other estimators based on depth…
Reconciliation enforces coherence between hierarchical forecasts, in order to satisfy a set of linear constraints. While most works focus on the reconciliation of the point forecasts, we consider probabilistic reconciliation and we analyze…
Rank and PIT histograms are established tools to assess the calibration of probabilistic forecasts. They not only check whether an ensemble forecast is calibrated, but they also reveal what systematic biases (if any) are present in the…
Statistical hypotheses are translations of scientific hypotheses into statements about one or more distributions, often concerning their centre. Tests that assess statistical hypotheses of centre implicitly assume a specific centre, e.g.,…
A user-focused verification approach for evaluating probability forecasts of binary outcomes (also known as probabilistic classifiers) is demonstrated that is (i) based on proper scoring rules, (ii) focuses on user decision thresholds, and…
Parameter estimation via M- and Z-estimation is equally powerful in semiparametric models for one-dimensional functionals due to a one-to-one relation between corresponding loss and identification functions via integration and…
Parameter estimation in linear errors-in-variables models typically requires that the measurement error distribution be known (or estimable from replicate data). A generalized method of moments approach can be used to estimate model…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
We are concerned with obtaining well-calibrated output distributions from regression models. Such distributions allow us to quantify the uncertainty that the model has regarding the predicted target value. We introduce the novel concept of…
We study estimation of a multivariate function $f:{\bf R}^d \to {\bf R}$ when the observations are available from function $Af$, where $A$ is a known linear operator. Both the Gaussian white noise model and density estimation are studied.…
Calibration$\unicode{x2014}$the problem of ensuring that predicted probabilities align with observed class frequencies$\unicode{x2014}$is a basic desideratum for reliable prediction with machine learning systems. Calibration error is…
Many supervised machine learning tasks, such as future state prediction in dynamical systems, require precise modeling of a forecast's uncertainty. The Multiple Hypotheses Prediction (MHP) approach addresses this problem by providing…
A central problem in computational statistics is to convert a procedure for sampling combinatorial from an objects into a procedure for counting those objects, and vice versa. Weconsider sampling problems coming from *Gibbs distributions*,…