Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series A, Pt. 1 , pp. 77--89

RATES OF BOOTSTRAP APPROXIMATION FOR THE MEAN OF LATTICE VARIABLES

By

S. N. LAHIRI, *Iowa State University*

SUMMARY. It is shown that even for the mean of lattice variables, bootstrap approximation is second order correct in a suitable metric which metrizes the topology of the weak convergence on **R**. In addition, almost sure rates of bootstrap approximation for normalized sample means of i.i.d. lattice random variables are established in the cases where the error of approximation is measured in the Lévy metric and in the bounded Lipschitz metric.

*AMS (1980) subject classification.* Primary 60G50; secondary 62G05.

*Key words and phrases.* Bootstrap, bounded Lipschitz metric, Edgeworth expansion, lattice random variables, Lévy metric.