We prove weak convergence of triangular arrays to the compound Poisson limit using Tihomirov's method. The result is applied to statistical estimation of the threshold parameter in autoregressive models.where α(n) ≥ 0 is a decreasing sequence with lim n→∞ α(n) = 0 (A3) for a measurable function |v(x)| ≤ 1, x ∈ R n−j+1