We introduce a methodology based on the Luria–Delbrück fluctuation model for estimating the cell kinetics of clonally expanding populations. In particular, this approach allows estimation of the net cell proliferation rate, the extinction coefficient and the initial (viable) population size. We present a systematic approach based on spatial partitioning, which captures the local fluctuations of the number and sizes of individual clones. However, partitioning introduces measurement error by inflating the number of clones, which is dependent on time and the degree of cell migration. We perform various in silico experiments to explore the properties of the estimators and we show that there exists a direct relationship between precision and observation time. We also explore the trade-off between the measurement error and the estimation accuracy. By exploring different scales of cellular fluctuations, from the entire population down to those of individual clones, we show that this methodology is useful for inferring important parameters in neoplastic progression.