Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7547538 | Journal of Statistical Planning and Inference | 2016 | 33 Pages |
Abstract
Semi-parametric tail index estimators, such as the Hill, Harmonic Moment, Pickands, and Dekkers, Einmahl and de Haan estimators, rely upon a tuning parameter that typically grows with sample size n. Proper selection of this tuning parameter k=k(n) is crucial for good practical performance, although asymptotic theory dictates that 1/k+k/nâ0 as nââ. A similar issue presents itself in the bandwidth literature in spectral density estimation and recent research shows that the use of asymptotic distributions when the bandwidth is a fixed ratio of sample size yields improved approximations to finite-sample distributions. Here, we study some semi-parametric tail index estimators utilizing the same perspective where k=bn and bâ(0,1) is a fixed constant. This allows us to derive asymptotic bias and variance expressions which are compatible with the small-b conventional theory. Our simulations corroborate that the finite-sample bias and variance are well described by the asymptotic bias and variance quantities arising from our fixed bandwidth ratio theory.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Tucker McElroy, Chaitra H. Nagaraja,