Asymptotic Behaviors and Confidence Intervals for the Number of Operating Sensors in a Sensor Network

In this paper, we study asymptotic behaviors of an estimator of the number of operating sensors in a sensor network based on the Good-Turing estimator. The asymptotic normality, some moderate deviations and deviation inequalities of the estimator are obtained. Our approach is based on the tail probability estimates and moderate deviations for occupancy problems. Applying these asymptotic behaviors, we give a performance analysis for the estimator of the number <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> of operating nodes when the deviations of the estimator are in <inline-formula> <tex-math notation="LaTeX">$(\sqrt {N}, o(N))$ </tex-math></inline-formula>. These estimates also provide a method to build confidence interval of <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula>.