Convergence on randomly trimmed sums with a dependent sample (Q1266281)

A central limit theorem and a strong law of large numbers are established for randomly trimmed sums \(T_n=\sum^{\beta_n}_{i=\alpha_n+1}X_{ni}\) of the order statistics \((X_{ni})\) of a \(\varphi\)-mixing sequence of random variables \((X_n)\), where \(\alpha_n\) and \(\beta_n\) are positive integer valued random variables such that \(\alpha_n/n\) and \(\beta_n/n\) converge to random variables \(0\leq\alpha<\beta\leq 1\).