The law of the iterated logarithm and central limit theorem for L-statistics

The Chung-Smirnov law of the iterated logarithm and the Finkelstein functio nal law of the iterated logarithm for empirical processes are used to estab lish new results on the central limit theorem, the law of the iterated loga rithm, and the strong law of largo numbers for L-statistics with certain bo unded and smooth weight functions. These results are used to obtain necessa ry and sufficient conditions for almost sure convergence and for convergenc e in distribution of some well-known L-statistics and U-statistics, includi ng Gini's mean difference statistic. A law of the logarithm for weighted su ms of order statistics is also presented. (C) 2001 Academic Press.