Minimum Scoring Rule Inference

By A. P. Dawid, Monica Musio, Laura Ventura. 2014

79 citations recorded by the source corpus.

Proper scoring rules are devices for encouraging honest assessment of probability distributions. Just like log‐likelihood, which is a special case, a proper scoring rule can be applied to supply an unbiased estimating equation for any statistical model, and the theory of such equations can be applied to understand the properties of the associated estimator. In this paper, we discuss some novel applications of scoring rules to parametric inference. In particular, we focus on scoring rule test statistics, and we propose suitable adjustments to allow reference to the usual asymptotic chi‐squared distribution. We further explore robustness and interval estimation properties, by both theory and simulations.

Subfields: Artificial Intelligence, Information Systems

View Paper: https://www.semanticscholar.org/paper/3d86b9b5c2950aa6b1b6b976810f2ce283c4bc99

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Citations in the corpus

Functional peaks‐over‐threshold analysis (2020, methodology): “Functional threshold exceedances were studied using r(X) = sups∈S X(s) by Ferreira and de Haan (2014) for continuous processes, but this functional treats as extreme all events with an exceedance at at least one location and requires that x(s) is observed throughout S.”
Of quantiles and expectiles: consistent scoring functions, Choquet representations and forecast rankings (2015, background): “Now (see Dawid et al. (2016)), given any proper scoring rule SÅ, and a parametric family F ={Fθ}, we can construct an associated M-estimator of θ.”
Generative Adversarial Nets from a Density Ratio Estimation Perspective (2016, methodology): “It is more robust than under KL divergence [43, 8].”
Using Stacking to Average Bayesian Predictive Distributions (with Discussion) (2017, background): “See Dawid (1986); Dawid and Sebastiani (1999); Grünwald and Dawid (2004); Parry et al. (2012); Dawid and Musio (2014, 2015); Dawid et al. (2016) for a variety of theory, examples and applications.”
Theory and applications of proper scoring rules (2014, background): “Expression (19), together with the fact that boundedness of f ′ implies boundedness of f (see Dawid et al. (2014)), suggest the following sufficient conditions for B-robustness: Condition 1 1. f ′(u) is bounded.”