On the self-similar nature of Ethernet traffic (extended version)
IEEE/ACM Transactions on Networking (TON)
Matrix computations (3rd ed.)
SIAM Journal on Scientific Computing
A comparison of estimators for 1/f noise
Physica D
Generalized Fourier and Toeplitz Results for Rational Orthonormal Bases
SIAM Journal on Control and Optimization
Choosing Regularization Parameters in Iterative Methods for Ill-Posed Problems
SIAM Journal on Matrix Analysis and Applications
Computational Statistics & Data Analysis - Special issue: Computational econometrics
Toeplitz and circulant matrices: a review
Communications and Information Theory
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Hi-index | 22.14 |
There is significant interest in long-range dependent processes since they occur in a wide range of phenomena across different areas of study. Based on the available models capable of describing long-range dependence, various parameter estimation methods have been developed. In this paper we revisit the maximum likelihood estimator and its computationally efficient approximations: Whittle's Estimator and the Circulant Embedding Estimator. In particular, this paper proves the asymptotic properties of the Circulant Embedding estimator and establishes the asymptotic equivalence between the three estimators. Furthermore, it is shown that the three methods are ill-conditioned and thus highly sensitive to the presence of measurement errors. Finally, we introduce a regularisation method that improves the performance of the maximum likelihood methods when the datasets have been largely contaminated with errors.