Abstract
Abstract We introduce a location-scale model for conditional heavy-tailed distributions when the covariate is deterministic. First, nonparametric estimators of the location and scale functions are introduced. Second, an estimator of the conditional extreme-value index is derived. The asymptotic properties of the estimators are established under mild assumptions and their finite sample properties are illustrated both on simulated and real data.
Highlights
The literature on extreme-value analysis of independent and identically distributed observations is very elaborate, see for instance [3, 12, 26]
We introduce a location-scale model for conditional heavy-tailed distributions when the covariate is deterministic
The asymptotic properties of the estimators are established under mild assumptions and their nite sample properties are illustrated both on simulated and real data
Summary
The literature on extreme-value analysis of independent and identically distributed observations is very elaborate, see for instance [3, 12, 26]. The nite-sample performance of the estimators of the location and scale functions as well as of the conditional tail-index are illustrated on simulated data from model (4). The estimation accuracy of the location and scale function does not seem to be sensitive to ν, see Figure 1(b,c)–3(b,c) This trend was expected, since the conditional second-order parameter is the main driver of the bias, as explained, and since |ρ| = /( ν) for a Student distribution.
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