Power transformations to induce normality and their applications

• 成果类型: Article
• 署名作者: Chen, WW; Deo, RS
• 署名单位: Texas A&M University System; Texas A&M University College Station; New York University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2004.00435.x
• 发表日期: 2004
• 页码: 117-130
• 关键词: time-series models; fit; tests; form

摘要

Random variables which are positive linear combinations of positive independent random variables can have heavily right-skewed finite sample distributions even though they might be asymptotically normally distributed. We provide a simple method of determining an appropriate power transformation to improve the normal approximation in small samples. Our method contains the Wilson-Hilferty cube root transformation for chi(2) random variables as a special case. We also provide some important examples, including test statistics of goodness-of-fit and tail index estimators, where such power transformations can be applied. In particular, we study the small sample behaviour of two goodness-of-fit tests for time series models which have been proposed recently in the literature. Both tests are generalizations of the popular Box-Ljung-Pierce portmanteau test, one in the time domain and the other in the frequency domain. A power transformation with a finite sample mean and variance correction is proposed, which ameliorates the small sample effect. It is found that the corrected versions of the tests have markedly better size properties. The correction is also found to result in an overall increase in power which can be significant under certain alternatives. Furthermore, the corrected tests also have better power than the Box-Ljung-Pierce portmanteau test, unlike the uncorrected versions.