Broadcast audience estimation

We investigate the estimation of the size of a broadcast audience. We give the maximum likelihood (ML) estimators for different scenarios. Using a Poisson approximation we obtain upper and lower bounds for the audience size. The ML estimators has closed-form expressions, so do the bounds. We treat the problem of a malfunctioning feedback flow control, where the sender is overwhelmed by feedback messages. The ML estimate of the audience size is obtained using the expectation-maximization (EM) algorithm, even under such conditions as censored values due to feedback implosion. Quantifying the influence of feedback implosion on the loss of information for the audience estimation, we further investigate the choice of the parameters in order to optimize estimation results