| J. Beran (1986). "Estimation, testing and prediction for self-similar and related processes," Ph.D Thesis, ETH, Zurich. |
....the normal distribution [DS86, P94] Without this test, we must question whether it is valid to use Whittle s estimator (previous item) Both Beran s test and Whittle s estimator (Eqn. 3) are intricately tied to the estimated power spectrum of the process. For an FGN process, the power spectrum is [B86]: f( H) A( H) Theta jj Gamma2H Gamma1 B( H) 4) for 0 H 1 and Gamma , where: A( H) 2 sin( H ) Gamma(2H 1) 1 Gamma cos ) B( H) 1 X j=1 Theta (2 j ) Gamma2H Gamma1 (2 j Gamma ) Gamma2H Gamma1 The main difficulty with using Eqn. 4 to compute ....
J. Beran, "Estimation, Testing and Prediction for Self-Similar and Related Processes", Ph.D. dissertation, ETH, Zurich, 1986.
....3. The Mathematics of Self Similarity 13 Eq. 3.8 holds it is easily shown that var(X (m) bm Gamma1 ; as m 1 (3.13) where b is a finite positive constant independent of m. This has serious implications for classical statistical tests and the calculation of confidence intervals (see [B86] and [HRRS86] since the usual measures of standard deviation are wrong by a factor that tends to infinity as the sample size increases. Chapter 4 Dealing With Self Similarity By now the attentive reader will be under the impression that self similarity is an abstract concept given that the ....
J. Beran, "Estimation, Testing and Prediction for Self-Similar and Related Processes," PhD Thesis, ETH Zurich, Switzerland, 1986
....for the normal distribution [DS86, PF94] Without this test, we cannot know that it is valid to use Whittle s estimator (previous item) Both Beran s test and Whittle s estimator (Eqn.3) are intricately tied to the estimated power spectrum of the process. For an FGN process, the power spectrum is [B86]: f( H) A( H) 2 jj 02H01 B( H) 3 (4) for 0 H 1 and 0 , where: A( H) 2 sin( H)0(2H 1) 1 0 cos ) B( H) 1 X j=1 2 (2 j ) 02H01 (2 j 0 ) 02H01 3 Themain difficulty with using Eqn. 4 to compute the power spectrum is the vexing infinite summation in the ....
J. Beran, "Estimation, Testing and Prediction for Self-Similar and Related Processes", Ph.D. dissertation, ETH, Zurich, 1986.
No context found.
J. Beran (1986). "Estimation, testing and prediction for self-similar and related processes," Ph.D Thesis, ETH, Zurich.
No context found.
J. Beran (1986). "Estimation, testing and prediction for self-similar and related processes," Ph.D Thesis, ETH, Zurich.
No context found.
J. Beran, "Estimation, Testing and Prediction for Self-Similar and Related Processes", PhD Thesis, ETH Zurich, Switzerland, 1986.
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