Network dimensioning is an important issue to provide stable and QoS-rich communication services. A reliable estimation of bandwidths of links between the end-to-end path is a first step towards the network dimensioning. Pathchar is one of such tools for the bandwidth estimation for every link between two end hosts. However, pathchar still has several problems. If unexpectedly large errors are included or if route alternation is present during the measurement, the obtained estimation is much far from the correct one. We investigate the method to eliminate those errors in estimating the bandwidth. To increase the reliability on the estimation, the confidence interval for the estimated bandwidth is important. For this purpose, two approaches, parametric and nonparametric approaches, are investigated to add the confidence intervals. Another important issue is the method for controlling the measurement period to eliminate the measurement overheads. In this paper, we propose a measurement method to adaptively control the number of measurement data sets. Through experimental results, we show that our statistical approaches can provide the robust estimation regardless of the network conditions.