Detection of non-Gaussianity

References

• Graham P, Turok N, Lubin PM, Schuster JA. A simple test for non-Gaussianity in cosmic microwave background radiation measurements. Astrophys J. 1995;449:404–412. doi: 10.1086/176065
   Web of Science ®Google Scholar
• Jin J, Starck J-L, Donoho DL, Aghanim N, Forni O. Cosmological non-Gaussian signature detection: comparing performance of different statistical tests. EURASIP J Appl Signal Process. 2005;15:2470–2485. doi: 10.1155/ASP.2005.2470
   Google Scholar
• Güner B, Frankford MT, Johnson JT. A study of the Shapiro-Wilk test for the detection of pulsed sinusoidal radio frequency interference. IEEE Trans Geosc Rem Sens. 2009;47:1745–1751. doi: 10.1109/TGRS.2008.2006906
   Web of Science ®Google Scholar
• Romão X, Delgado R, Costa A. An empirical power comparison of univariate goodness-of-fit tests for normality. J Statist Comput Simul. 2010;80:545–591. doi: 10.1080/00949650902740824
   Web of Science ®Google Scholar
• Tarongi JM, Camps A. Normality analysis for RFI detection in microwave radiometry. Remote Sens. 2010;2:191–210. doi: 10.3390/rs2010191
   Web of Science ®Google Scholar
• Shapiro SS, Wilk MB. An analysis of variance test for normality (complete samples). Biometrika. 1965;52:591–611. doi: 10.1093/biomet/52.3-4.591
   Web of Science ®Google Scholar
• Brown BM, Hettmansperger TP. Normal scores, normal plots, and tests for normality. J Am Statist Assoc. 1996;91:1668–1675.
   Web of Science ®Google Scholar
• LaRiccia VN. Optimal goodness-of-fit tests for normality against skewness and kurtosis alternatives. J Statist Plan Inference. 1986;13:67–79. doi: 10.1016/0378-3758(86)90120-5
   Web of Science ®Google Scholar
• Chen L, Shapiro SS. An alternative test for normality based on normalized spacings. J Statist Comput Simul. 1995;53:269–288. doi: 10.1080/00949659508811711
   Web of Science ®Google Scholar
• Del Barrio E, Cuesta-Albertos JA, Matrán C, Rodríguez-Rodríguez JM. Tests of goodness of fit based on the L2-Wasserstein distance. Ann Statist. 1999;27:1230–1239. doi: 10.1214/aos/1017938923
   Web of Science ®Google Scholar
• Shapiro SS, Francia RS. An approximate analysis of variance test for normality. J Am Statist Assoc. 1972;67:215–216. doi: 10.1080/01621459.1972.10481232
   Web of Science ®Google Scholar
• De Wet T, Venter JH. Asymptotic distributions of certain test criteria of normality. S Afr Statist J. 1972;6:135–149.
   Google Scholar
• Aly E-EAA, M Csörgodblac. Quadratic nuisance-parameter-free goodness-of-fit tests in the presence of location and scale parameters. Canad J Statist. 1985;13:53–70. doi: 10.2307/3315167
   Web of Science ®Google Scholar
• LaRiccia VN, Mason DM. Cramér-von Mises statistics based on the sample quantile function and estimated parameters. J Multivar Anal. 1986;18:93–106. doi: 10.1016/0047-259X(86)90061-8
   Web of Science ®Google Scholar
• Puri ML, Rao CR. Augmenting Shapiro–Wilk test for normality. In: Walter Joh. Ziegler, editor. Contributions to applied statistics, a festschrift to A. Linder. New York: Birkhäuser; 1976. p. 129–139.
   Google Scholar
• LaBrecque J. Goodness-of-fit tests based on nonlinearity in probability plots. Technometrics. 1977;19:293–306. doi: 10.1080/00401706.1977.10489551
   Web of Science ®Google Scholar
• LaRiccia VN. Smooth goodness-of-fit tests: A quantile function approach. J Am Statist Assoc. 1991;86:427–431. doi: 10.1080/01621459.1991.10475060
   Web of Science ®Google Scholar
• Donoho DL, Jin J. Higher criticism for detecting sparse heterogeneous mixtures. Ann Statist. 2004;32:962–994. doi: 10.1214/009053604000000265
   Web of Science ®Google Scholar
• LaRiccia VN, Mason DM. Optimal goodness-of-fit tests for location/scale families of distributions based on the sum of squares of L-statistics. Ann Statist. 1985;13:315–330. doi: 10.1214/aos/1176346595
   Web of Science ®Google Scholar
• Ledwina T. Data-driven version of Neyman's smooth test of fit. J Amer Statist Assoc. 1994;89:1000–1005. doi: 10.1080/01621459.1994.10476834
   Web of Science ®Google Scholar
• Inglot T, Ledwina T. Intermediate approach to comparison of some goodness-of-fit-tests. Ann Inst Statist Math. 2001;53:810–834. doi: 10.1023/A:1014669423096
   Web of Science ®Google Scholar
• Krauczi É. A study of the quantile correlation test for normality. TEST. 2009;18:156–165. doi: 10.1007/s11749-007-0074-6
   Web of Science ®Google Scholar
• Rogers WH, Tukey JW. Understanding some long-tailed symmetrical distributions. Statist Neerlandica. 1972;26:211–226. doi: 10.1111/j.1467-9574.1972.tb00191.x
   Google Scholar
• Inglot T, Jurlewicz T, Ledwina T. On Neyman-type smooth tests of fit. Statistics. 1990;21:549–568. doi: 10.1080/02331889008802265
   Google Scholar
• Shapiro SS, Wilk MB, Chen HJ. A comparative study of various tests for normality. J Am Statist Assoc. 1968;63:1343–1372. doi: 10.1080/01621459.1968.10480932
   Web of Science ®Google Scholar
• Gan FF, Koehler KJ. Goodness-of-fit tests based on P–P probability plots. Technometrics. 1990;32:289–303.
   Web of Science ®Google Scholar
• Cai TT, Jeng XJ, Jin J. Optimal detection of heterogeneous and heteroscedastic mixtures. J R Statist Soc B. 2011;73:629–662. doi: 10.1111/j.1467-9868.2011.00778.x
   Google Scholar
• De Roo RD, Misra S, Ruf CS. Sensitivity of the kurtosis statistic as a detector of pulsed sinusoidal RFI. IEEE Trans Geosc Remote Sens. 2007;45:1938–1946. doi: 10.1109/TGRS.2006.888101
   Web of Science ®Google Scholar
• Bai ZD, Chen L. Weighted W test for normality and asymptotics: a revisit of Chen-Shapiro test for normality. J Statist Plann Inference. 2003;113:485–503. doi: 10.1016/S0378-3758(02)00110-6
   Web of Science ®Google Scholar
• Chen L. C470. Normality tests based on weighted order statistics. J Statist Comput Simul. 2003;73:603–606. doi: 10.1080/0094965031000138173
   Web of Science ®Google Scholar
• Grabchak M, Samorodnitsky G. Do financial returns have finite or infinite variance? A paradox and an explanation. Quant Financ. 2010;10:883–893. doi: 10.1080/14697680903540381
   Web of Science ®Google Scholar
• Andrews DF, Herzberg AM. Data: a collection of problems from many fields for student and research worker. New York: Springer; 1985.
   Google Scholar
• Bowman A, Azzalini A. Applied smoothing techniques for data analysis: the kernel approach with S-plus illustrations. Oxford: Clarendon Press; 1997.
   Google Scholar
• Jaeschke D. The asymptotic distribution of the supremum of the standardized empirical distribution function on subintervals. Ann Statist. 1979;7:108–115. doi: 10.1214/aos/1176344558
   Web of Science ®Google Scholar
• Eicker F. The asymptotic distribution of the suprema of the standardized empirical processes. Ann Statist. 1979;7:116–138. doi: 10.1214/aos/1176344559
   Web of Science ®Google Scholar
• Révész P. A joint study of the Kolmogorov–Smirnov and the Eicker–Jaeschke statistics. Statist Decis. 1982;1:57–65.
   Google Scholar
• De Wet T. Goodness-of-fit tests for location and scale families based on a weighted L2-Wasserstein distance measure. TEST. 2002;11:89–107. doi: 10.1007/BF02595731
   Web of Science ®Google Scholar
• S Csörgodblac. Weighted correlation tests for location-scale families. Math Comput Model. 2003;38:753–762. doi: 10.1016/S0895-7177(03)90059-8
   Web of Science ®Google Scholar