A note on the normal approximation error for randomly weighted self-normalized sums

Let X = {Xn}n≥1 and Y = {Yn}n≥1 be two independent random sequences. We obtain rates of convergence to the normal law of randomly weighted self-normalized sums (formula presented.). These rates are seen to hold for the convergence of a number of important statistics, such as for instance Student's t-statistic or the empirical correlation coefficient. © 2013 Akadémiai Kiadó, Budapest, Hungary.SCOPUS: ar.j