Mathematical Properties of Continuous Ranked Probability Score
Forecasting
- URL: http://arxiv.org/abs/2205.04360v1
- Date: Mon, 9 May 2022 15:01:13 GMT
- Title: Mathematical Properties of Continuous Ranked Probability Score
Forecasting
- Authors: Romain Pic and Cl\'ement Dombry and Philippe Naveau and Maxime
Taillardat
- Abstract summary: We study the rate of convergence in terms of CRPS of distributional regression methods.
We show that the k-nearest neighbor method and the kernel method for the distributional regression reach the optimal rate of convergence in dimension $dgeq2$.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The theoretical advances on the properties of scoring rules over the past
decades have broaden the use of scoring rules in probabilistic forecasting. In
meteorological forecasting, statistical postprocessing techniques are essential
to improve the forecasts made by deterministic physical models. Numerous
state-of-the-art statistical postprocessing techniques are based on
distributional regression evaluated with the Continuous Ranked Probability
Score (CRPS). However, theoretical properties of such minimization of the CRPS
have mostly considered the unconditional framework (i.e. without covariables)
and infinite sample sizes. We circumvent these limitations and study the rate
of convergence in terms of CRPS of distributional regression methods We find
the optimal minimax rate of convergence for a given class of distributions.
Moreover, we show that the k-nearest neighbor method and the kernel method for
the distributional regression reach the optimal rate of convergence in
dimension $d\geq2$ and in any dimension, respectively.
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