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Kernel Type Estimator and Statistical Properties for Intensity Function of Periodic Poisson Process with Power Function Trend

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Author(s): Ro’fah Nur Rachmawati

Journal: Journal of Mathematics and Statistics
ISSN 1549-3644

Volume: 8;
Issue: 3;
Start page: 403;
Date: 2012;
Original page

Keywords: Unbiased estimator | intensity function | several nonparametric methods | asymptotic normality | statistical properties

ABSTRACT
Problem statement: In this study, we construct the estimation for a periodic component of the intensity function of a periodic Poisson process in the presence of power function trend by using the general kernel function. Beside that we also construct the statistical properties of the estimator. Approach: It is considered the worst case where there is only available a single realization of the Poisson process having intensity which consist of a periodic component and a power function trend, observed in the interval [0, n]. It is assumed that the period of the periodic component and the slope of the power function trend are known. Results: It has been formulated the estimator and asymptotic approximations to the bias and variance of the estimator. Conclusion: The estimator that we construct is asymptotically unbiased estimator for a periodic component of the intensity function of a periodic Poisson process in the presence of a power function trend.
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