On the uniform consistency of frequency polygons for ψ-mixing samples

In this article, the frequency polygon investigated by Scott (1985) is studied as a nonparametric estimator for ψ-mixing samples. Under mild conditions, we prove the uniformly strong consistency of the estimator and obtain the corresponding rate of convergence which is nearly equal to the one obtained by Carbon et al. (1997) and, our results weaken the relevant conditions used by Carbon et al. (1997). In addition, the uniformly weak consistency is also given.