Tapered Block Bootstrap for Unit Root Testing

Abstract

A new bootstrap procedure for unit root testing based on the tapered block bootstrap is introduced. This procedure is similar to previous tests that were based on the block bootstrap and stationary bootstrap, but it has the advantage of the tapering procedure that has been previously shown to reduce the bias of the variance estimator by an order of magnitude. In this paper, the procedure is defined including a specific data-driven method for choosing the block size. Both theoretical results for the asymptotic behavior of the test as well as simulations which address the small sample properties and are used for comparison to other methods are given.

Reliability estimation for drive axle of wheel loader under extreme small sample

“…26 The Bootstrap method cannot be used if the sample size is 1 or 2; the computational results could be either arbitrary or the confidence interval was enlarged if the sample size is 3 or 4. Although Bootstrap resampling method has been improved in some of the recent literatures, [27][28][29] it is still not working for extreme small sample problem. For Bayesian inference method, the underlying working theory is that evidence or observations are used to update or newly infer the probability that a hypothesis may be true.…”