DEVELOPMENT OF A NOVEL SELECTION CRITERION FOR OPTIMUM CHOICE OF “M”IN THE “M- OUT -OF- N” BOOTSTRAP

Efron (1979) introduced the n-out-of-n bootstrap, which is indeed an important tool for statistical inference and has wide spread applications. However, there are situations, where the n-out-of-n bootstrap is not consistent. Thus, the m-out-of-n bootstrap was introduced to overcome the problem. It reduces the computational burden associated with bootstrapping. But, the problem with m-out-of-n bootstrap is the choice of m, which is one of the important aspects in bootstrapping. In this paper, we study criteria for choosing best value of m in m-out-of-n bootstrapping in linear regression. This is a pure computational study that gives general criteria for optimizing m in m-out of-n bootstrap, under which the chosen m ( ) behaves properly.