ON TAIL INDEX ESTIMATION FOR DEPENDENT, HETEROGENEOUS DATA
研究了Hill尾部指数估计量在相依异质过程中的渐近性质，提出了新的极值相依度量，证明了估计量的一致性和渐近正态性，并给出了渐近方差的非参数估计。
In this paper we analyze the asymptotic properties of the popular distribution tail index estimator by Hill (1975) for dependent, heterogeneous processes. We develop new extremal dependence measures that characterize a massive array of linear, nonlinear, and conditional volatility processes with long or short memory. We prove that the Hill estimator is weakly and uniformly weakly consistent for processes with extremes that form mixingale sequences and asymptotically normal for processes with extremes that are near epoch dependent (NED) on some arbitrary mixing functional. The extremal persistence assumptions in this paper are known to hold for mixing, L p -NED, and some non- L p -NED processes, including ARFIMA, FIGARCH, explosive GARCH, nonlinear ARMA-GARCH, and bilinear processes, and nonlinear distributed lags like random coefficient and regime-switching autoregressions. Finally, we deliver a simple nonparametric estimator of the asymptotic variance of the Hill estimator and prove consistency for processes with NED extremes.