Generalised least squares estimation of regularly varying space-time processes based on flexible observation schemes
| Autor: | Sven Buhl, Claudia Klüppelberg |
|---|---|
| Přispěvatelé: | Lehrstuhl für Mathematische Statistik |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Mathematical optimization Economics Econometrics and Finance (miscellaneous) Asymptotic distribution Mathematics - Statistics Theory Statistics Theory (math.ST) 01 natural sciences Domain (mathematical analysis) 010104 statistics & probability Consistency (statistics) Brown-Resnick process Extremogram Generalised least squares estimation Max-stable process Observation schemes Regularly varying process Semiparametric estimation Space-time process 0502 economics and business FOS: Mathematics Applied mathematics 050207 economics 0101 mathematics ddc:510 Engineering (miscellaneous) Mathematics Parametric statistics 60F05 60G70 62F12 62G32 37A25 62M30 62P12 Estimation theory Stochastic process Space time 05 social sciences Sample size determination Mathematik |
| Popis: | Regularly varying stochastic processes model extreme dependence between process values at different locations and/or time points. For such processes we propose a two-step parameter estimation of the extremogram, when some part of the domain of interest is fixed and another increasing. We provide conditions for consistency and asymptotic normality of the empirical extremogram centred by a pre-asymptotic version for such observation schemes. For max-stable processes with Fr{\'e}chet margins we provide conditions, such that the empirical extremogram (or a bias-corrected version) centred by its true version is asymptotically normal. In a second step, for a parametric extremogram model, we fit the parameters by generalised least squares estimation and prove consistency and asymptotic normality of the estimates. We propose subsampling procedures to obtain asymptotically correct confidence intervals. Finally, we apply our results to a variety of Brown-Resnick processes. A simulation study shows that the procedure works well also for moderate sample sizes. Comment: 37 pages, 18 Figures and 3 Tables |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|