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A bootstrap procedure in linear regression with nonstationary errors
Author(s) -
Yeh Arthur B.
Publication year - 1998
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315680
Subject(s) - estimator , consistency (knowledge bases) , mathematics , context (archaeology) , statistics , least squares function approximation , generalized least squares , strong consistency , block (permutation group theory) , linear regression , ordinary least squares , variance (accounting) , non linear least squares , standard error , regression , combinatorics , paleontology , geometry , accounting , business , biology
In the context of linear regression with dependent and nonstationary errors, the classical moving‐block bootstrap (MBB) fails to capture the nonstationarity of the errors. A new bootstrap procedure called the blocking external bootstrap (BEB) is proposed to overcome the problem. The consistency of the BEB in estimating the variance of the least‐squares estimator is studied in the case of α‐mixing and nonstationary sequence of errors. It is shown that the BEB only achieves partial correction if the block size is fixed. Complete consistency is achieved by the BEB when the block size is allowed to go to infinity. We also study the first‐order consistency of the least squares estimator based on the BEB. A simulation study is carried out to assess the performance of the BEB versus the MBB in estimating the variance of the least‐squares estimator. Finally, some open problems are discussed.