Kernel Type Estimator and Statistical Properties for Intensity Function ofPeriodic Poisson Process with Power Function Trend | Science Publications

Journal of Mathematics and Statistics

Ro’fah Nur Rachmawati¹ 

关键词: Unbiased estimator;    intensity function;    several nonparametric methods;    asymptotic normality;    statistical properties;   

DOI  :  10.3844/jmssp.2012.403.412

学科分类：社会科学、人文和艺术（综合）

来源: Science Publications

【 摘 要 】

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.

【 授权许可】

Unknown