Size-Dependent Probability Bounds for t-Tests

The paper extends Chebyshev’s inequality to incorporate moments’ convergence in t-tests of model parameters. Size-dependent probability bounds are derived from one conditional higher-order moment of the distribution of the test statistic. Monte Carlo simulations attest that, in the cases of heteroskedastic and autocorrelated observations, the proposed bounds over-reject less than the asymptotic approximation and bootstrap methods. Therefore, when asymptotic critical values are suspected to lead to the over-rejection of the null hypothesis, the proposed inequalities may be used in conjunction to bootstrap methods to reduce the number of instances in which multiple re-samplings and associated estimations have to be performed.