Skewness and kurtosis as locally best invariant tests of normality
| dc.creator | Takemura, Akimichi | |
| dc.creator | Matsui, Muneya | |
| dc.creator | Kuriki, Satoshi | |
| dc.date | 2006-08-20 | |
| dc.date.accessioned | 2026-07-07T08:08:07Z | |
| dc.date.available | 2026-07-07T08:08:07Z | |
| dc.description | Consider testing normality against a one-parameter family of univariate distributions containing the normal distribution as the boundary, e.g., the family of $t$-distributions or an infinitely divisible family with finite variance. We prove that under mild regularity conditions, the sample skewness is the locally best invariant (LBI) test of normality against a wide class of asymmetric families and the kurtosis is the LBI test against symmetric families. We also discuss non-regular cases such as testing normality against the stable family and some related results in the multivariate cases. | |
| dc.identifier | https://arxiv.org/abs/math/0608499 | |
| dc.identifier | http://arxiv.org/abs/math/0608499 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131151 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62G10 | |
| dc.title | Skewness and kurtosis as locally best invariant tests of normality | |
| dc.type | text |