Related papers: Point forecasting and forecast evaluation with gen…
In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…
The paper considers an Euler discretization based numerical scheme for approximating functionals of invariant distribution of an ergodic diffusion. Convergence of the numerical scheme is shown for suitably chosen discretization step, and a…
Reconstruction of a function from noisy data is often formulated as a regularized optimization problem over an infinite-dimensional reproducing kernel Hilbert space (RKHS). The solution describes the observed data and has a small RKHS norm.…
Forecasting is an indispensable element of operational research (OR) and an important aid to planning. The accurate estimation of the forecast uncertainty facilitates several operations management activities, predominantly in supporting…
Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…
This paper considers the problem of estimating the cumulative distribution function and probability density function of a random variable using data quantized by uniform and non-uniform quantizers. A simple estimator is proposed based on…
Demand forecasting in competitive, uncertain business environments requires models that can integrate multiple evaluation perspectives rather than being restricted to hyperparameter optimization based on a single metric. This traditional…
Conformal prediction is a learning framework controlling prediction coverage of prediction sets, which can be built on any learning algorithm for point prediction. This work proposes a learning framework named conformal loss-controlling…
We propose notions of calibration for probabilistic forecasts of general multivariate quantities. Probabilistic copula calibration is a natural analogue of probabilistic calibration in the univariate setting. It can be assessed empirically…
Every observation may follow a distribution that is randomly selected in a class of distributions. It is called the distribution uncertainty. This is a fact acknowledged in some research fields such as financial risk measure. Thus, the…
Machine learning predictions are typically interpreted as the sum of contributions of predictors. Yet, each out-of-sample prediction can also be expressed as a linear combination of in-sample values of the predicted variable, with weights…
Measurement error is an important problem that has not been very well studied in the context of Functional Data Analysis. To the best of our knowledge, there are no existing methods that address the presence of functional measurement errors…
We introduce a Loss Discounting Framework for model and forecast combination which generalises and combines Bayesian model synthesis and generalized Bayes methodologies. We use a loss function to score the performance of different models…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
We study the problem of estimating the joint probability mass function (pmf) over two random variables. In particular, the estimation is based on the observation of $m$ samples containing both variables and $n$ samples missing one fixed…
Expectile regression is a nice tool for investigating conditional distributions beyond the conditional mean. It is well-known that expectiles can be described with the help of the asymmetric least square loss function, and this link makes…
This paper analyzes a popular loss function used in machine learning called the log-cosh loss function. A number of papers have been published using this loss function but, to date, no statistical analysis has been presented in the…
A general method to combine several estimators of the same quantity is investigated. In the spirit of model and forecast averaging, the final estimator is computed as a weighted average of the initial ones, where the weights are constrained…
Uncertainty representation and quantification are paramount in machine learning and constitute an important prerequisite for safety-critical applications. In this paper, we propose novel measures for the quantification of aleatoric and…
This paper studies loss functions for finite sets. For a given finite set $S$, we give sum-of-square type loss functions of minimum degree. When $S$ is the vertex set of a standard simplex, we show such loss functions have no spurious…