On Berry–Esséen bound of frequency polygon estimation under $$\rho $$ ρ -mixing samples

The frequency polygon estimation, which is based on histogram technique, has similar convergence rate as those of non-negative kernel estimators and the advantages of computational simplicity. This work will study the Berry–Esséen bound of frequency polygon estimation with $$\rho $$ ρ -mixing samples under some general conditions. The rates are shown to be $$O(n^{-1/9})$$ O ( n - 1 / 9 ) if the mixing coefficients decay polynomially and $$O(n^{-1/6}\log ^{1/3}n)$$ O ( n - 1 / 6 log 1 / 3 n ) if the mixing coefficients decay geometrically. These results improve and extend the corresponding ones in the literature and reveal that the frequency polygon estimator also has similar Berry–Esséen bound as those of kernel estimators. Moreover, some numerical analysis is also presented to assess the finite sample performance of the theoretical results.