arXiv subjects

Xiaochun Meng

Publications and source records attributed to Xiaochun Meng.

4 recordsLinked to original sources

arXiv2025

Angular Combining of Forecasts of Probability Distributions

When multiple forecasts are available for a probability distribution, forecast combining enables a pragmatic synthesis of the information to extract the wisdom of the crowd. The linear opinion pool has been widely used, whereby the combining is applied to the probabilities of the distributional forecasts. However, it has been argued that this will tend to deliver overdispersed distributions, prompting the combination to be applied, instead, to the quantiles of the distributional forecasts. Results from different applications are mixed, leaving it as an empirical question whether to combine probabilities or quantiles. In this paper, we present an alternative approach. Looking at the distributional forecasts, combining the probabilities can be viewed as vertical combining, with quantile combining seen as horizontal combining. Our proposal is to allow combining to take place on an angle between the extreme cases of vertical and horizontal combining. We term this angular combining. The angle is a parameter that can be optimized using a proper scoring rule. For implementation, we provide a pragmatic numerical approach and a simulation algorithm. Among our theoretical results, we show that, as with vertical and horizontal averaging, angular averaging results in a distribution with mean equal to the average of the means of the distributions that are being combined. We also show that angular averaging produces a distribution with lower variance than vertical averaging, and, under certain assumptions, greater variance than horizontal averaging. We provide empirical results for distributional forecasts of Covid mortality, macroeconomic survey data, and electricity prices.

stat.ME↗

arXiv2023

Scores for Multivariate Distributions and Level Sets

Forecasts of multivariate probability distributions are required for a variety of applications. Scoring rules enable the evaluation of forecast accuracy, and comparison between forecasting methods. We propose a theoretical framework for scoring rules for multivariate distributions, which encompasses the existing quadratic score and multivariate continuous ranked probability score. We demonstrate how this framework can be used to generate new scoring rules. In some multivariate contexts, it is a forecast of a level set that is needed, such as a density level set for anomaly detection or the level set of the cumulative distribution as a measure of risk. This motivates consideration of scoring functions for such level sets. For univariate distributions, it is well-established that the continuous ranked probability score can be expressed as the integral over a quantile score. We show that, in a similar way, scoring rules for multivariate distributions can be decomposed to obtain scoring functions for level sets. Using this, we present scoring functions for different types of level set, including density level sets and level sets for cumulative distributions. To compute the scores, we propose a simple numerical algorithm. We perform a simulation study to support our proposals, and we use real data to illustrate usefulness for forecast combining and CoVaR estimation.

math.ST↗

arXiv2021

Targetting Kollo Skewness with Random Orthogonal Matrix Simulation

Modelling multivariate systems is important for many applications in engineering and operational research. The multivariate distributions under scrutiny usually have no analytic or closed form. Therefore their modelling employs a numerical technique, typically multivariate simulations, which can have very high dimensions. Random Orthogonal Matrix (ROM) simulation is a method that has gained some popularity because of the absence of certain simulation errors. Specifically, it exactly matches a target mean, covariance matrix and certain higher moments with every simulation. This paper extends the ROM simulation algorithm presented by Hanke et al. (2017), hereafter referred to as HPSW, which matches the target mean, covariance matrix and Kollo skewness vector exactly. Our first contribution is to establish necessary and sufficient conditions for the HPSW algorithm to work. Our second contribution is to develop a general approach for constructing admissible values in the HPSW. Our third theoretical contribution is to analyse the effect of multivariate sample concatenation on the target Kollo skewness. Finally, we illustrate the extensions we develop here using a simulation study.

stat.CO↗

arXiv2021

Evaluating the Discrimination Ability of Proper Multivariate Scoring Rules

Proper scoring rules are commonly applied to quantify the accuracy of distribution forecasts. Given an observation they assign a scalar score to each distribution forecast, with the the lowest expected score attributed to the true distribution. The energy and variogram scores are two rules that have recently gained some popularity in multivariate settings because their computation does not require a forecast to have parametric density function and so they are broadly applicable. Here we conduct a simulation study to compare the discrimination ability between the energy score and three variogram scores. Compared with other studies, our simulation design is more realistic because it is supported by a historical data set containing commodity prices, currencies and interest rates, and our data generating processes include a diverse selection of models with different marginal distributions, dependence structure, and calibration windows. This facilitates a comprehensive comparison of the performance of proper scoring rules in different settings. To compare the scores we use three metrics: the mean relative score, error rate and a generalised discrimination heuristic. Overall, we find that the variogram score with parameter p=0.5 outperforms the energy score and the other two variogram scores.

stat.ME↗