A powerful and interpretable alternative to the Jarque-Bera test of normality based on 2nd-power skewness and kurtosis, using the Rao's score test on the APD family

被引:31
作者
Desgagne, A. [1 ]
de Micheaux, P. Lafaye [2 ]
机构
[1] Univ Quebec Montreal, Dept Math, Montreal, PQ, Canada
[2] UNSW Sydney, Sch Math & Stat, Sydney, NSW 2052, Australia
基金
加拿大自然科学与工程研究理事会;
关键词
Normality test; asymmetric power distribution; Lagrange multiplier test; Rao's score test; skewness; kurtosis; OF-FIT TESTS; OMNIBUS TEST; REGRESSION; UNIVARIATE;
D O I
10.1080/02664763.2017.1415311
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
We introduce the 2nd-power skewness and kurtosis, which are interesting alternatives to the classical Pearson's skewness and kurtosis, called 3rd-power skewness and 4th-power kurtosis in our terminology. We use the sample 2nd-power skewness and kurtosis to build a powerful test of normality. This test can also be derived as Rao's score test on the asymmetric power distribution, which combines the large range of exponential tail behavior provided by the exponential power distribution family with various levels of asymmetry. We find that our test statistic is asymptotically chi-squared distributed. We also propose a modified test statistic, for which we show numerically that the distribution can be approximated for finite sample sizes with very high precision by a chi-square. Similarly, we propose a directional test based on sample 2nd-power kurtosis only, for the situations where the true distribution is known to be symmetric. Our tests are very similar in spirit to the famous Jarque-Bera test, and as such are also locally optimal. They offer the same nice interpretation, with in addition the gold standard power of the regression and correlation tests. An extensive empirical power analysis is performed, which shows that our tests are among the most powerful normality tests. Our test is implemented in an package called PoweR.
引用
收藏
页码:2307 / 2327
页数:21
相关论文
共 24 条
[1]   A TEST OF GOODNESS OF FIT [J].
ANDERSON, TW ;
DARLING, DA .
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1954, 49 (268) :765-769
[2]  
[Anonymous], 1993, Continuous Univariate Distributions, DOI DOI 10.1016/0167-9473(96)90015-8
[3]  
[Anonymous], 2001, The Laplace Distributionand Generalizations: A Revisit With Applications to Communications,Economics, Engineering, and Finance
[4]   A test of normality with high uniform power [J].
Bonett, DG ;
Seier, E .
COMPUTATIONAL STATISTICS & DATA ANALYSIS, 2002, 40 (03) :435-445
[5]   OMNIBUS TEST CONTOURS FOR DEPARTURES FROM NORMALITY BASED ON SQUARE-ROOT B1 AND B2 [J].
BOWMAN, KO ;
SHENTON, LR .
BIOMETRIKA, 1975, 62 (02) :243-250
[6]   An alternative test for normality based on normalized spacings [J].
Chen, L ;
Shapiro, SS .
JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 1995, 53 (3-4) :269-287
[7]   A goodness-of-fit test for normality based on polynomial regression [J].
Coin, Daniele .
COMPUTATIONAL STATISTICS & DATA ANALYSIS, 2008, 52 (04) :2185-2198
[8]   TESTS FOR DEPARTURE FROM NORMALITY - EMPIRICAL RESULTS FOR DISTRIBUTIONS OF B2 AND SQUARE ROOT B1 [J].
DAGOSTIN.R ;
PEARSON, ES .
BIOMETRIKA, 1973, 60 (03) :613-622
[9]  
de Micheaux PL, 2016, J STAT SOFTW, V69, P1
[10]  
Del Barrio E, 1999, ANN STAT, V27, P1230