| Paper: | SPTM-P12.6 | ||
| Session: | Estimation | ||
| Time: | Friday, May 21, 13:00 - 15:00 | ||
| Presentation: | Poster | ||
| Topic: | Signal Processing Theory and Methods: Detection, Estimation, and Class. Thry & Apps. | ||
| Title: | GOOD-TURING ESTIMATION OF THE NUMBER OF OPERATING SENSORS: A LARGE DEVIATIONS ANALYSIS | ||
| Authors: | Cristian Budianu; Cornell University | ||
| Lang Tong; Cornell University | |||
| Abstract: | The paper \cite{Budianu&Tong:03ASILOMAR} proposes an estimator for the number of operating sensors in a wireless sensor network based on the Good-Turing non-parametric estimator of the missing mass. This paper investigates the performance of this estimator using the theory of large deviations. We determine the asymptotic behavior of the rate function as the ratio $n/N$ between the number of collected samples $n$ and the number of operating sensors $N$ decreases to zero. The simulations reveal that the confidence intervals obtained using the large deviations formula are upper bounds for the actual performance of the estimator. Together with the asymptotic behavior of the rate function, this suggests the surprising fact that if the scaling law $n=f(N)$ is used for the number of samples, then reliable estimation can be done if $n$ grows at least as fast as $\sqrt{N}$. Separately, it is shown that if $\lim_{N\rightarrow\infty}\frac{n}{\sqrt{N}}=0$ the estimator can't be used. | ||
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