Details
| Original language | English |
|---|---|
| Article number | 106276 |
| Number of pages | 21 |
| Journal | Journal of Statistical Planning and Inference |
| Volume | 238 |
| Early online date | 8 Feb 2025 |
| Publication status | E-pub ahead of print - 8 Feb 2025 |
Abstract
Conditional excess distribution modelling is a widely used technique, in financial and insurance mathematics or survival analysis, for instance. Classical theory considers the thresholds as fixed values. In contrast, the use of empirical quantiles as thresholds offers advantages with respect to the design of the statistical experiment. Either way, the modeller is in a non-standard situation and runs in the risk of improper usage of statistical procedures. From both points of view, statistical planning and inference, a detailed discussion is requested. For this purpose, we treat both methods and demonstrate the necessity taking into account the characteristics of the approaches in practice. In detail, we derive general statements for empirical processes related to the conditional excess distribution in both situations. As examples, estimating the mean excess and the conditional Value-at-Risk are given. We apply our findings for the testing problems of goodness-of-fit and homogeneity for the conditional excess distribution and obtain new results of outstanding interest.
Keywords
- Conditional excess distribution, Empirical quantile, Goodness-of-fit test, Homogeneity test
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
- Mathematics(all)
- Applied Mathematics
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In: Journal of Statistical Planning and Inference, Vol. 238, 106276, 09.2025.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Fixed values versus empirical quantiles as thresholds in excess distribution modelling
AU - Gaigall, Daniel
AU - Gerstenberg, Julian
N1 - Publisher Copyright: © 2025 The Authors
PY - 2025/2/8
Y1 - 2025/2/8
N2 - Conditional excess distribution modelling is a widely used technique, in financial and insurance mathematics or survival analysis, for instance. Classical theory considers the thresholds as fixed values. In contrast, the use of empirical quantiles as thresholds offers advantages with respect to the design of the statistical experiment. Either way, the modeller is in a non-standard situation and runs in the risk of improper usage of statistical procedures. From both points of view, statistical planning and inference, a detailed discussion is requested. For this purpose, we treat both methods and demonstrate the necessity taking into account the characteristics of the approaches in practice. In detail, we derive general statements for empirical processes related to the conditional excess distribution in both situations. As examples, estimating the mean excess and the conditional Value-at-Risk are given. We apply our findings for the testing problems of goodness-of-fit and homogeneity for the conditional excess distribution and obtain new results of outstanding interest.
AB - Conditional excess distribution modelling is a widely used technique, in financial and insurance mathematics or survival analysis, for instance. Classical theory considers the thresholds as fixed values. In contrast, the use of empirical quantiles as thresholds offers advantages with respect to the design of the statistical experiment. Either way, the modeller is in a non-standard situation and runs in the risk of improper usage of statistical procedures. From both points of view, statistical planning and inference, a detailed discussion is requested. For this purpose, we treat both methods and demonstrate the necessity taking into account the characteristics of the approaches in practice. In detail, we derive general statements for empirical processes related to the conditional excess distribution in both situations. As examples, estimating the mean excess and the conditional Value-at-Risk are given. We apply our findings for the testing problems of goodness-of-fit and homogeneity for the conditional excess distribution and obtain new results of outstanding interest.
KW - Conditional excess distribution
KW - Empirical quantile
KW - Goodness-of-fit test
KW - Homogeneity test
UR - http://www.scopus.com/inward/record.url?scp=85217259437&partnerID=8YFLogxK
U2 - 10.1016/j.jspi.2025.106276
DO - 10.1016/j.jspi.2025.106276
M3 - Article
AN - SCOPUS:85217259437
VL - 238
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
SN - 0378-3758
M1 - 106276
ER -