Lucien Birge and Pascal Massart. Estimation of Integral Functionals of a Density. *The Annals of Statistics*, 23(1):11–29, 1995. doi: 10.1214/aos/1176324452. URL https://doi.org/10.1214/aos/1176324452.

K.P. Burnham and D.R. Anderson. *Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach*. Springer New York, 2007. ISBN 9780387224565.

W.G. Cochran. *Sampling Techniques, 3Rd Edition*. A Wiley publication in applied statistics. Wiley India Pvt. Limited, 2007. ISBN 9788126515240.

Richard Davis and Sidney Resnick. Tail Estimates Motivated by Extreme Value Theory. *The Annals of Statistics*, 12(4):1467–1487, 1984. doi: 10.1214/aos/1176346804. URL https://doi.org/10.1214/aos/1176346804.

L. de Haan and A. Ferreira. *Extreme Value Theory: An Introduction*. Springer Series in Operations Research and Financial Engineering. Springer New York, 2007. ISBN 9780387344713.

A. L. M. Dekkers, J. H. J. Einmahl, and L. De Haan. A Moment Estimator for the Index of an Extreme-Value Distribution. *The Annals of Statistics*, 17(4):1833–1855, 1989. doi: 10.1214/aos/1176347397. URL https://doi.org/10.1214/aos/1176347397.

Arnold L. M. Dekkers and Laurens De Haan. On the Estimation of the Extreme-Value Index and Large Quantile Estimation. *The Annals of Statistics*, 17(4):1795–1832, 1989. doi: 10.1214/aos/1176347396. URL https://doi.org/10.1214/aos/1176347396.

P. Embrechts, C. Klüppelberg, and T. Mikosch. *Modelling Extremal Events: for Insurance and Finance*. Stochastic Modelling and Applied Probability. Springer Berlin Heidelberg, 2013. ISBN 9783540609315.

R. A. Fisher and L. H. C. Tippett. Limiting forms of the frequency distribution of the largest or smallest member of a sample. *Proceedings of the Cambridge Philosophical Society*, 24 (2):180, January 1928.

J. Galambos and E. Seneta. Regularly varying sequences. *Proceedings of the American Mathematical Society*, 41(1):110–116, 1973. ISSN 00029939, 10886826.

B. Gnedenko. Sur la distribution limite du terme maximum d'une serie aleatoire. *Annals of Mathematics*, 44(3):423–453, 1943. ISSN 0003486X.

Clifford M. Hurvich and Chih-Ling Tsai. Regression and time series model selection in small samples. *Biometrika*, 76(2):297–307, 06 1989. ISSN 0006-3444.

Max Kuhn and Kjell Johnson. *Applied predictive modeling*. Springer, New York, NY, 2013. ISBN 9781461468493 1461468493 1461468485 9781461468486. URL http://www.amazon.com/Applied-Predictive-Modeling-Max-Kuhn/dp/1461468485/.

T. Mikosch, Operations Research EURANDOM European Institute for Statistics, Probability, and their Applications. *Regular Variation, Subexponentiality and Their Applications in Probability Theory*. EURANDOM report. Eindhoven University of Technology, 1999.
Lucien Birge and Pascal Massart. Estimation of Integral Functionals of a Density. *The Annals of Statistics*, 23(1):11–29, 1995. doi: 10.1214/aos/1176324452. URL https://doi.org/10.1214/aos/1176324452.

K.P. Burnham and D.R. Anderson. *Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach*. Springer New York, 2007. ISBN 9780387224565.

W.G. Cochran. *Sampling Techniques, 3Rd Edition*. A Wiley publication in applied statistics. Wiley India Pvt. Limited, 2007. ISBN 9788126515240.

Richard Davis and Sidney Resnick. Tail Estimates Motivated by Extreme Value Theory. *The Annals of Statistics*, 12(4):1467–1487, 1984. doi: 10.1214/aos/1176346804. URL https://doi.org/10.1214/aos/1176346804.

L. de Haan and A. Ferreira. *Extreme Value Theory: An Introduction*. Springer Series in Operations Research and Financial Engineering. Springer New York, 2007. ISBN 9780387344713.

A. L. M. Dekkers, J. H. J. Einmahl, and L. De Haan. A Moment Estimator for the Index of an Extreme-Value Distribution. *The Annals of Statistics*, 17(4):1833–1855, 1989. doi: 10.1214/aos/1176347397. URL https://doi.org/10.1214/aos/1176347397.

Arnold L. M. Dekkers and Laurens De Haan. On the Estimation of the Extreme-Value Index and Large Quantile Estimation. *The Annals of Statistics*, 17(4):1795–1832, 1989. doi: 10.1214/aos/1176347396. URL https://doi.org/10.1214/aos/1176347396.

P. Embrechts, C. Klüppelberg, and T. Mikosch. *Modelling Extremal Events: for Insurance and Finance*. Stochastic Modelling and Applied Probability. Springer Berlin Heidelberg, 2013. ISBN 9783540609315.

R. A. Fisher and L. H. C. Tippett. Limiting forms of the frequency distribution of the largest or smallest member of a sample. *Proceedings of the Cambridge Philosophical Society*, 24 (2):180, January 1928.

J. Galambos and E. Seneta. Regularly varying sequences. *Proceedings of the American Mathematical Society*, 41(1):110–116, 1973. ISSN 00029939, 10886826.

B. Gnedenko. Sur la distribution limite du terme maximum d'une serie aleatoire. *Annals of Mathematics*, 44(3):423–453, 1943. ISSN 0003486X.

Clifford M. Hurvich and Chih-Ling Tsai. Regression and time series model selection in small samples. *Biometrika*, 76(2):297–307, 06 1989. ISSN 0006-3444.

Max Kuhn and Kjell Johnson. *Applied predictive modeling*. Springer, New York, NY, 2013. ISBN 9781461468493 1461468493 1461468485 9781461468486. URL http://www.amazon.com/Applied-Predictive-Modeling-Max-Kuhn/dp/1461468485/.

T. Mikosch, Operations Research EURANDOM European Institute for Statistics, Probability, and their Applications. *Regular Variation, Subexponentiality and Their Applications in Probability Theory*. EURANDOM report. Eindhoven University of Technology, 1999.
Jerzy Neyman. On the two different aspects of the representative method: The method of stratified sampling and the method of purposive selection. *Journal of the Royal Statistical Society*, 97(4):558–625, 1934. ISSN 09528385.

James Pickands. Statistical Inference Using Extreme Order Statistics. *The Annals of Statistics*, 3(1):119 – 131, 1975.

Gideon Schwarz. Estimating the Dimension of a Model. *The Annals of Statistics*, 6(2):461 – 464, 1978.

M. Stone. An asymptotic equivalence of choice of model by cross-validation and akaike's criterion. *Journal of the Royal Statistical Society. Series B (Methodological)*, 39(1):44–47, 1977. ISSN 00359246. URL http://www.jstor.org/stable/2984877.

Mervyn Stone. Crossvalidatory choice and assessment of statistical predictions. *Journal of the royal statistical society series b-methodological*, 36:111–133, 1976. URL https://api.semanticscholar.org/CorpusID:62698647.

Ya Su, Youjian Zhao, Chenhao Niu, Rong Liu, Wei Sun, and Dan Pei. Robust anomaly detection for multivariate time series through stochastic recurrent neural network. In *Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining*, KDD '19, page 28282837, New York, NY, USA, 2019. Association for Computing Machinery. ISBN 9781450362016.

Nariaki Sugiura. Further analysts of the data by Akaike's information criterion and the finite corrections. *Communications in Statistics - Theory and Methods*, 7(1):13–26, 1978.

Renjie Wu and Eamonn J. Keogh. Current time series anomaly detection benchmarks are flawed and are creating the illusion of progress. *CoRR*, abs/2009.13807, 2020.
Jerzy Neyman. On the two different aspects of the representative method: The method of stratified sampling and the method of purposive selection. *Journal of the Royal Statistical Society*, 97(4):558–625, 1934. ISSN 09528385.

James Pickands. Statistical Inference Using Extreme Order Statistics. *The Annals of Statistics*, 3(1):119 – 131, 1975.

Gideon Schwarz. Estimating the Dimension of a Model. *The Annals of Statistics*, 6(2):461 – 464, 1978.

M. Stone. An asymptotic equivalence of choice of model by cross-validation and akaike's criterion. *Journal of the Royal Statistical Society. Series B (Methodological)*, 39(1):44–47, 1977. ISSN 00359246. URL http://www.jstor.org/stable/2984877.

Mervyn Stone. Crossvalidatory choice and assessment of statistical predictions. *Journal of the royal statistical society series b-methodological*, 36:111–133, 1976. URL https://api.semanticscholar.org/CorpusID:62698647.

Ya Su, Youjian Zhao, Chenhao Niu, Rong Liu, Wei Sun, and Dan Pei. Robust anomaly detection for multivariate time series through stochastic recurrent neural network. In *Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining*, KDD '19, page 28282837, New York, NY, USA, 2019. Association for Computing Machinery. ISBN 9781450362016.

Nariaki Sugiura. Further analysts of the data by Akaike's information criterion and the finite corrections. *Communications in Statistics - Theory and Methods*, 7(1):13–26, 1978.

Renjie Wu and Eamonn J. Keogh. Current time series anomaly detection benchmarks are flawed and are creating the illusion of progress. *CoRR*, abs/2009.13807, 2020.