A Note on Estimation for Gamma and Stable Processes
本文推导了基于跳跃大小≥ε的极大似然估计量在ε趋近于0时的渐近分布，针对非递减纯跳跃伽马过程和稳定过程，并指出稳定过程估计量一致而伽马过程不一致。
Maximum likelihood estimators of the parameters of nondecreasing pure-jump gamma and stable processes based on the jumps of size greater than or equal to ε were studied in a previous paper (Basawa & Brockwell, 1978). In particular, for a single realization {X( u ), 0 ≤ u ≤ t }, the estimators for the stable process are consistent as ε ↓ 0, but this is not so for the gamma process. In the present note we derive asymptotic distributions as ε ↓ 0 for these estimators, centred and scaled as appropriate.