Asymptotic Statistical Theory for the Samples Problems using the Functional Empirical Process, revisited I

TL;DR

This paper develops an asymptotic theory for sample problems using the functional empirical process, providing a new method that performs well with sample sizes around 15 or more, and compares favorably to Gaussian methods.

Contribution

It introduces a general sample problem approach based on the functional empirical process, extending estimation theory for means, variances, and ratios, with validation against Gaussian methods.

Findings

Results are nearly equivalent to Gaussian methods for sample size 10.

Estimation of mean differences is highly accurate for larger samples.

The method is effective for samples of size 15 or more, requiring finite fourth moments.

Abstract

In this paper we study the asymptotic theory for samples problem based on the functional empirical process (fep), this new method is called general samples problem. We suggest this method to develop the full theory of estimation of means, variances, ratios of variances and difference of means for independent samples. We compare the results of our new method to the Gaussian method using simulated and real data. The obtained results are almost equivalent to those in the Gaussian case for samples's size equal to $10$. It has been prove that the estimation of the means difference is very precise regardless of the equality or inequality of variances for greater sizes of sample. This method is recommended when the sizes of samples is around or greater that $15$ and it requires the finiteness of the fourth order moment.