Size-Dependent Probability Bounds for t-Tests

摘要

The paper extends Chebyshev’s inequality to incorporate moments’ conver- gencein t-tests of model parameters. Size-dependent probability bounds are derived fromone conditional higher-order moment of the distribution of the test statistic. MonteCarlo simulations attest that, in the cases of heteroskedastic and autocorrelatedobservations, the proposed bounds over-reject less than the asymptoticapproximation and bootstrap methods. Therefore, when asymp- totic critical valuesare suspected to lead to the over-rejection of the null hy- pothesis, the proposedinequalities may be used in conjunction to bootstrap methods to reduce the numberof instances in which multiple re-samplings and associated estimations have to beperformed.