Analytical Study for Periodic Functions and Estimation | ||||
| The Egyptian Statistical Journal | ||||
| Article 6, Volume 49, Issue 1, June 2005, Page 74-92 PDF (16.31 MB) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/esju.2005.313557 | ||||
 View on SCiNiTO | ||||
| Author | ||||
| Laila A. Khalil* | ||||
| Cairo University | ||||
| Abstract | ||||
| In this article we consider a real process xTwhich is composed of a real function mT() and a white brownian noise UT. where the real function mT() represents a linear combination of known periodic functions ₁,….., k and some unknown parameters =(₁,...,k). We use the maximum likelihood method to estimate the unknown parameters. We proved a theorem which gives an upper bound for the probability that the absolute value of the Euclidian distance between the parameters and its estimators exceeds a small positive value ɛ. Some examples of periodic functions and the convergence of its sequence of means are given. Computation is performed for periodic functions i's of the form i(x)=sin ix. As application of periodic function we exposed MACHO project in the domain of astronomy. | ||||
| Keywords | ||||
| White Brownian Noise - Time Series - Periodic Function; Periodicity; Periodogram - Maximum Likelihood Method - MACHO Project | ||||
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