We prove an optimal asymptotic result for weighted Lp-distance of partial sum processes of independent identically distributed random variables. Using this result, we prove also the convergence in distribution of weighted Lp-functionals of U-statistic type processes which are used in change-point analysis.

changepoint problem, Gaussian processes, Lp-distance, partial sums, random integrals, U-statistics, weight functions
dx.doi.org/10.1016/0304-4149(93)90076-G
Stochastic Processes and their Applications
School of Mathematics and Statistics

Szyszkowicz, B. (1993). Lp-approximations of weighted partial sum processes. Stochastic Processes and their Applications, 45(2), 295–308. doi:10.1016/0304-4149(93)90076-G