A general method for estimating standard errors

Abstract

This paper is concerned with the estimation of standard errors of location estimates associated with distribution-free test statistics. There are two popular approaches to this problem. The first of these is based on resampling methods like the bootstrap and jackknife. The second is based on properties of the relevant estimating equations and generally involve the estimation of gradients and the choice of a smoothing parameter. We propose a new completely general standard error estimation method, known as the translation method, which does not involbe resampling nor the user to specify the value of smoothing parameter. We show that the resulting variance estimator is asymptotically equivalent to a kernel quantile estimator with a specific bandwidth. The translation method is simple requiring just the null distribution of the test statistic and the values at which the test statistic changes. As such, it is envisaged that unlike other methods, the translation method could be used in statistical software packages to produce default standard error estimates in a wide variety of situations.

Keywords:

• Estimating equations
• Kernel quantile estimators
• resampling
• standard error