Error estimation in the method of quasi-optimal weights

TL;DR

This paper analyzes how to improve confidence interval accuracy in the method of quasi-optimal weights for small samples by developing criteria and correction methods for asymptotic and non-linear effects.

Contribution

It introduces analytical criteria and correction methods to address distortions in confidence intervals caused by small sample sizes in the quasi-optimal weights method.

Findings

Developed a criterion for the validity of asymptotic normality assumptions.

Derived a correction method for systematic shifts due to non-linearity.

Numerical example demonstrating the effectiveness of the corrections.

Abstract

We examine the problem of construction of confidence intervals within the basic single-parameter, single-iteration variation of the method of quasi-optimal weights. Two kinds of distortions of such intervals due to insufficiently large samples are examined, both allowing an analytical investigation. First, a criterion is developed for validity of the assumption of asymptotic normality together with a recipe for the corresponding corrections. Second, a method is derived to take into account the systematic shift of the confidence interval due to the non-linearity of the theoretical mean of the weight as a function of the parameter to be estimated. A numerical example illustrates the two corrections.