Abstract: Let {Xn, n≥1} be an m-widely orthant dependence (m-WOD) sequence with the same distribution, f_n(x) and r_n(x) were the kernel estimators of the density function f(x) and the failure rate function based on the sample X₁,X₂,…,X_n, respectively. Under some suitable assumptions, we proved the strong consistency and the uniform strong consistency of the kernel density estimator and failure rate function kernel estimator by using the moment inequality for m-WOD sequence and BorelCantelli lemma.

Key words: m-WOD sequence, kernel estimator, failure rate function, (uniform) strong consistency