Inference about the mean of a skewed population: a comparative study
We consider the problem of hypotheses testing and interval estimation of the mean of a possibly skewed population. The usual procedures based on the large sample distribution of the studentized sample mean can be imprecise because of the violation of the nominal values of test sizes or confidence levels. Many attempts were made to overcome this problem. Most of them are based on correcting the studentized t-variable with higher order terms and possibly using the bootstrap to set critical values. Another approach is based on the empirical likelihood and possibly using the bootstrap or the Bartlett correction to improve the calibration. In this article, using simulation techniques, we investigate and compare these competing approaches in terms of the attainment of the nominal values of test sizes, confidence levels and the powers of the associated tests. It is found that intervals based on the Bartlett-corrected empirical likelihood are very accurate even for small sample sizes from highly skewed populations. Its power performance is also comparable and in many ways better than the other procedures considered, besides its applicability for testing when all other procedures fail to attain the nominal sizes of the tests.
skewed population empirical likelihood bartlett correction t-test population mean