Necessary and sufficient conditions for the moving blocks bootstrap central limit theorem of the mean

Abstract

For strictly stationary sequences X _i , we study the relations between statistics Z _n =n ^−1/2∑ (X _i −EX _i ) and its Bootstrap counterpart We establish sufficient and necessary conditions for Central Limit Theorem in this setting and generalise the cases for which converges to Gaussian limit, while Z _n fails to do so. In addition, we establish Bootstrap Central Limit Theorem without mixing conditions and identify the cases for which and Z _n are asymptotically close, while both fail to converge in distribution.

Keywords:

• bootstrap
• stationarity
• mean
• bootstrap