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Spectral Estimation for Random Processes with Stationary Increments
Başlık:
Spectral Estimation for Random Processes with Stationary Increments
Yazar:
Chen, Wei, author. (orcid)0000-0003-2769-7007
ISBN:
9780438092440
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (129 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-11(E), Section: B.
Advisors: Haimeng Zhang Committee members: Greg Bell; Xiaoli Gao; Sat Gupta; Scott Richter.
Özet:
In studying a stationary random process on R, the covariance function is commonly used to characterize the second-order spatial dependency. Through the inversion of Fourier transformation, its corresponding spectral density has been widely used to describe the periodical components and frequencies. When the process is with stationary dth increments, that is, when the resulting process after undertaken dth order of differences is stationary, the notion of structure function is put forward. Through the inversion formula, the spectrum can be represented by the structure function. In this dissertation, we first investigate the properties of the proposed Method of Moments structure function estimator, through which we obtain the spectral density function estimation of the underlying process. In particular, when the process is intrinsically stationary, which is also a process is with stationary increments of order 1, we derive the spectral density functions for commonly used variogram models. Furthermore, our proposed estimation method is applied to estimate the spectral density of power variogram models. All of the above results are supplemented via simulations and a real data analysis. Our results show that the proposed estimation method performs well in recovering the true spectral density function on various processes with stationary increments we considered.
Notlar:
School code: 0154
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(688929.1) | 688929-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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