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.
Khalil, L. (2005). Analytical Study for Periodic Functions and Estimation. The Egyptian Statistical Journal, 49(1), 74-92. doi: 10.21608/esju.2005.313557
MLA
Laila A. Khalil. "Analytical Study for Periodic Functions and Estimation", The Egyptian Statistical Journal, 49, 1, 2005, 74-92. doi: 10.21608/esju.2005.313557
HARVARD
Khalil, L. (2005). 'Analytical Study for Periodic Functions and Estimation', The Egyptian Statistical Journal, 49(1), pp. 74-92. doi: 10.21608/esju.2005.313557
VANCOUVER
Khalil, L. Analytical Study for Periodic Functions and Estimation. The Egyptian Statistical Journal, 2005; 49(1): 74-92. doi: 10.21608/esju.2005.313557
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