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@article{ref:sp_estimate,
	abstract = { A new characterization and interpretation of the Cox [Ann. Instit. Statist. Math., 37 (1985), pp. 271--288] smoothing spline score estimator is provided, which makes it possible to construct an efficient algorithm for computing this score estimator. On choosing the smoothing parameter, the author proposes adaptive information criteria that outperform conventional data-driven choice criteria based on the assumption of Gaussian innovation. A small Monte-Carlo experiment is performed to investigate the finite sample properties of the smoothing spline score estimator as compared to adaptive kernel and weighted kernel score estimators. It is demonstrated that the smoothing spline score estimator is more robust to distributional variation and that all forms of the adaptive information criteria for choosing the smoothing parameter outperform conventional data driven smoothing parameter choice methods based on the Gaussian innovation assumption. },
	author = {Ng, Pin T.},
	doi = {10.1137/0915061},
	eprint = {https://doi.org/10.1137/0915061},
	journal = {SIAM Journal on Scientific Computing},
	number = {5},
	pages = {1003-1025},
	title = {Smoothing Spline Score Estimation},
	url = {https://doi.org/10.1137/0915061},
	volume = {15},
	year = {1994},
	bdsk-url-1 = {https://doi.org/10.1137/0915061}}

@article{ref:sp_test,
	author = {Anil K. Bera and Pin T. Ng},
	doi = {10.1080/00949659508811678},
	eprint = {https://doi.org/10.1080/00949659508811678},
	journal = {Journal of Statistical Computation and Simulation},
	number = {3},
	pages = {273-287},
	publisher = {Taylor & Francis},
	title = {Tests for normality using estimated score function},
	url = {https://doi.org/10.1080/00949659508811678},
	volume = {52},
	year = {1995},
	bdsk-url-1 = {https://doi.org/10.1080/00949659508811678}}

@article{ref:sp_condition,
	author = {Cox, Dennis},
	doi = {10.1007/BF02481097},
	journal = {Annals of the Institute of Statistical Mathematics},
	month = {12},
	pages = {271-288},
	title = {A penalty method for nonparametric estimation of the logarithmic derivative of a density function},
	volume = {37},
	year = {1985},
	bdsk-url-1 = {https://doi.org/10.1007/BF02481097}}

@article{ref:ghoshuni,
	abstract = {SUMMARY A new graphical tool for checking normality of independently and identically distributed observations based on the third derivative T3 of the logarithm of the empirical moment-generating function is proposed. A significant departure of this function from the horizontal zero line is indicative of non-normality. Behaviour in the neighbourhood of 0 indicates the type of departure from the normal distribution. Examples show that the T3-method, when used in conjunction with the classical probability plot, can provide valuable insight into the data and be a powerful graphical tool.},
	author = {Ghosh, Sucharita},
	date-modified = {2023-12-13 09:43:01 -0500},
	doi = {https://doi.org/10.1111/j.2517-6161.1996.tb02108.x},
	journal = {Journal of the Royal Statistical Society: Series B (Methodological)},
	keywords = {empirical transforms, probability plots, testing normality},
	number = {4},
	pages = {691-702},
	title = {A New Graphical Tool to Detect Non-Normality},
	volume = {58},
	year = {1996},
	bdsk-url-1 = {https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/j.2517-6161.1996.tb02108.x},
	bdsk-url-2 = {https://doi.org/10.1111/j.2517-6161.1996.tb02108.x}}

@article{ref:ghoshmulti,
	abstract = {Based on the theory of spherical distributions, a multivariate version of Ghosh (1996)'s T3-plot (MT3-plot) to detect non-multinormality is proposed. New critical bands for the MT3-plot based on a Kolmogorov-Smirnov type statistic are recommended to substitute Ghosh's critical bands in multivariate cases. Monte Carlo study on the choice of the projection directions gives the conclusion that the power of the MT3-plot based on the proposed Kolmogorov-Smirnov type statistic against severe non-multinormality is generally high regardless of high dimension if the projection direction is properly chosen. An application of the MT3-plot to two real-life data sets verifies the efficiency of the MT3 in finding evidence of non-multinormality in high-dimensional data analysis.},
	author = {Kai-Tai Fang and Run-Ze Li and Jia-Juan Liang},
	doi = {https://doi.org/10.1016/S0167-9473(98)90147-5},
	issn = {0167-9473},
	journal = {Computational Statistics \& Data Analysis},
	keywords = {Graphical technique, Invariant statistics, Left-spherical matrix distribution, Test of multinormality, Spherical distribution},
	number = {4},
	pages = {371-386},
	title = {A multivariate version of Ghosh's T3-plot to detect non-multinormality},
	url = {https://www.sciencedirect.com/science/article/pii/S0167947398901475},
	volume = {28},
	year = {1998},
	bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0167947398901475},
	bdsk-url-2 = {https://doi.org/10.1016/S0167-9473(98)90147-5}}

@book{wicklin2013simulating,
	author = {Wicklin, R.},
	isbn = {9781612903323},
	publisher = {SAS Institute},
	title = {Simulating Data with SAS},
	url = {https://books.google.com/books?id=PC7WboXY2W0C},
	year = {2013},
	bdsk-url-1 = {https://books.google.com/books?id=PC7WboXY2W0C}}

@article{ref:modern_multivariate,
	author = {Siotani M. and T. Hayakawa and X. Fujikoshi},
	doi = {https://doi.org/10.1002/bimj.4710300739},
	eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/bimj.4710300739},
	journal = {Biometrical Journal},
	number = {7},
	pages = {873-873},
	title = {Modern Multivariate Statistical Analysis. A Graduate Course and Handbook, Vol. 9. American Sciences Press, Inc., Columbus, Ohio 1985, xiv, 759 pp., \$39.50},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/bimj.4710300739},
	volume = {30},
	year = {1988},
	bdsk-url-1 = {https://onlinelibrary.wiley.com/doi/abs/10.1002/bimj.4710300739},
	bdsk-url-2 = {https://doi.org/10.1002/bimj.4710300739}}

@misc{chen2021normality,
	archiveprefix = {arXiv},
	author = {Hao Chen and Yin Xia},
	eprint = {1904.05289},
	primaryclass = {stat.ME},
	title = {A Normality Test for High-dimensional Data based on a Nearest Neighbor Approach},
	year = {2021}}

@article{num_MC,
	author = {Mundfrom, Daniel and Schaffer, Jay and Kim, Myoung-Jin and Shaw, Dale and Thongteeraparp, Ampai and Preecha, P. and Supawan, Pornsin},
	doi = {10.22237/jmasm/1304222580},
	journal = {Journal of Modern Applied Statistical Methods},
	month = {05},
	pages = {19-28},
	title = {Number of Replications Required in Monte Carlo Simulation Studies: A Synthesis of Four Studies},
	volume = {10},
	year = {2011},
	bdsk-url-1 = {https://doi.org/10.22237/jmasm/1304222580}}
