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878 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 45, NO. 3, APRIL 1999 A Wavelet-Based Joint Estimator of the
 

Summary: 878 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 45, NO. 3, APRIL 1999
A Wavelet-Based Joint Estimator of the
Parameters of Long-Range Dependence
Darryl Veitch and Patrice Abry
Abstract--A joint estimator is presented for the two parame-
ters that define the long-range dependence phenomenon in the
simplest case. The estimator is based on the coefficients of a
discrete wavelet decomposition, improving a recently proposed
wavelet-based estimator of the scaling parameter [4], as well
as extending it to include the associated power parameter. An
important feature is its conceptual and practical simplicity, con-
sisting essentially in measuring the slope and the intercept of a
linear fit after a discrete wavelet transform is performed, a very
fast (O(n)) operation. Under well-justified technical idealizations
the estimator is shown to be unbiased and of minimum or close
to minimum variance for the scale parameter, and asymptoti-
cally unbiased and efficient for the second parameter. Through
theoretical arguments and numerical simulations it is shown that
in practice, even for small data sets, the bias is very small and
the variance close to optimal for both parameters. Closed-form

  

Source: Abry, Patrice - Laboratoire de Physique, Ecole Normale Supérieure de Lyon

 

Collections: Engineering