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A main goal of regression is to derive statistical conclusions on the conditional distribution of the output variable Y given the input values x. Two of the most important characteristics of a single distribution are location and scale.…

In order theory, a rank function measures the vertical "level" of a poset element. It is an integer-valued function on a poset which increments with the covering relation, and is only available on a graded poset. Defining a vertical measure…

Estimation of the mean and covariance parameters for functional data is a critical task, with local linear smoothing being a popular choice. In recent years, many scientific domains are producing multivariate functional data for which $p$,…

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 problem of identifying to which of a given set of classes objects belong is ubiquitous, occurring in many research domains and application areas, including medical diagnosis, financial decision making, online commerce, and national…

Learning systems match predicted scores to observations over some domain. Often, it is critical to produce accurate predictions in some subset (or region) of the domain, yet less important to accurately predict in other regions. We…

Score matching is an estimation procedure that has been developed for statistical models whose probability density function is known up to proportionality but whose normalizing constant is intractable, so that maximum likelihood is…

In machine learning, the choice of a learning algorithm that is suitable for the application domain is critical. The performance metric used to compare different algorithms must also reflect the concerns of users in the application domain…

Human decision-makers often receive assistance from data-driven algorithmic systems that provide a score for evaluating objects, including individuals. The scores are generated by a function (mechanism) that takes a set of features as input…

We consider component-wise equivariant estimation of order restricted location/scale parameters of a general bivariate distribution under quite general conditions on underlying distributions and the loss function. This paper unifies various…

In a binary classification problem the feature vector (predictor) is the input to a scoring function that produces a decision value (score), which is compared to a particular chosen threshold to provide a final class prediction (output).…

We characterize the full classes of M-estimators for semiparametric models of general functionals by formally connecting the theory of consistent loss functions from forecast evaluation with the theory of M-estimation. This novel…

When predicting future events, it is common to issue forecasts that are probabilistic, in the form of probability distributions over the range of possible outcomes. Such forecasts can be evaluated using proper scoring rules. Proper scoring…

The total loss function associated with a set of cross-sectional predictions, that is, estimates or forecasts, summarizes the set's overall accuracy. Its arguments are the individual cross-sectional units' loss functions. Under general…

There has been substantial recent work on methods for estimating the slope function in linear regression for functional data analysis. However, as in the case of more conventional finite-dimensional regression, much of the practical…

We study a pricing setting where each customer is offered a contextualized price based on customer and/or product features. Often only historical sales data are available, so we observe whether a customer purchased a product at the price…

Prediction models are often employed in estimating parameters of optimization models. Despite the fact that in an end-to-end view, the real goal is to achieve good optimization performance, the prediction performance is measured on its own.…

Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…

Score function estimation is the cornerstone of both training and sampling from diffusion generative models. Despite this fact, the most commonly used estimators are either biased neural network approximations or high variance Monte Carlo…

Scoring rules are an important tool for evaluating the performance of probabilistic forecasting schemes. In the binary case, scoring rules (which are strictly proper) allow for a decomposition into terms related to the resolution and to the…