We study a nonparametric regression model, where the explanatory variable is nonstationary dependent functional data and the response variable is scalar. Assuming that the explanatory variable is a nonstationary mixture of stationary processes and general conditions of dependence of the observations (implied in particular by weak dependence), we obtain the asymptotic normality of the Nadaraya-Watson estimator. Under some additional regularity assumptions on the regression function, we obtain asymptotic confidence intervals for the regression function. We apply this result to estimate the quality of service for an end-to-end connection on a network.

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This work addresses the estimation and calculation of the operating point of a network's link in a digital traffic network. The notion of operating point comes from Effective Bandwidth (EB) theory. The results are valid for a wide range of traffic types. This means that the statistical characteristics of the traffic may be very general. We show that, given a good EB estimator, the operating point, i.e. the values of time and space (or multiplexing) parameters in which the EB gives the asymptotic overflow probability, can also be accurately estimated. Imposing some regularity conditions, a consistent estimator and confidence intervals of the operating point are developed. These conditions are very general, and they are met by commonly used estimators as the averaging estimator presented in [2] or the Markov Fluid model estimator presented in [10]. Using a software package developed by our workgroup that estimates the EB and other relevant parameters from traffic traces, simulation results are compared with the analytical results, showing very good fitting.

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