Lepage test

In statistics, the Lepage test is an exactly distribution-free test (nonparametric test) for jointly monitoring the location (central tendency) and scale (variability) in two-sample treatment versus control comparisons. This is one of the most famous rank tests for the two-sample location-scale problem. The Lepage test statistic is the squared Euclidean distance of standardized Wilcoxon rank-sum test for location and the standardized Ansari–Bradley test for scale. The Lepage test was first introduced by Yves Lepage in 1971 in a paper in Biometrika.[1] A large number of Lepage-type tests exists in statistical literature for simultaneously testing location and scale shifts in case-control studies. The details may be found in the book: Nonparametric statistical tests: A computational approach.[2] Kössler, W.[3] in 2006 also introduced various Lepage type tests using some alternative score functions optimal for various distributions. Dr. Amitava Mukherjee and Dr. Marco Marozzi introduced a class of percentile modified version of the Lepage test.[4] An alternative to the Lepage-type tests is known as the Cucconi test proposed by Odoardo Cucconi in 1968.[5]

Conducting the Lepage test with R, an open-source software

Practitioners can apply the Lepage test using the pLepage function of the contributory package NSM3,[6] built under R software. Andreas Schulz and Markus Neuhäuser also provided detailed R code for computation of test statistic and p-value of the Lepage test[7] for the users.

Application in statistical process monitoring

In recent years, Lepage statistic is widely used statistical process monitoring and quality control. In a classical development, in 2012, Amitava Mukherjee, an Indian statistician, and Subhabrata Chakraborti, an American statistician of Indian origin, introduced a distribution-free Shewhart-type Phase-II monitoring scheme[8] (control chart) for simultaneously monitoring of location and scale parameter of a process using a test sample of fixed size, when a reference sample of sufficiently large size is available from an in-control population. Later in 2015, the same statisticians along with Shovan Chowdhury, proposed a distribution-free CUSUM-type Phase-II monitoring scheme[9] based on the Lepage statistic. In 2017, Mukherjee further designed an EWMA-type distribution-free Phase-II monitoring scheme[10] for joint monitoring of location and scale. In the same year, Mukherjee, with Marco Marozzi, an Italian statistician known for promoting the Cucconi test, came together to design Circular-Grid Lepage chart – a new type of joint monitoring scheme.[11]

Multisample version of the Lepage test

In 2005, František Rublìk introduced the multisample version of the original two-sample Lepage test.[12] This work recently emerge as the motivation behind the proposal of the Phase-I distribution-free Shewhart-type control chart for joint monitoring of location and scale.

gollark: Unfortunately, this is implemented poorly.
gollark: I don't really agree. It is not practical to guess what directly applicable skills will be needed in the future. It should teach general skills like learning independently fast, mathematical modelling, useful writing, languages, and that sort of thing.
gollark: It's actually possible to learn things yourself.
gollark: CVs are maaaybe suitable for teaching since I don't think there's that much to it but you can probably learn faster with good feedback.
gollark: "How to get a job" is very complex, but that just means school would teach it very uselessly and/or vaguely and/or outdatedly.

See also

References
  1. Lepage, Yves (April 1971). "A Combination of Wilcoxon's and Ansari-Bradley's Statistics". Biometrika. 58 (1): 213–217. doi:10.2307/2334333. ISSN 0006-3444. JSTOR 2334333.
  2. Neuhäuser, Markus (2011-12-19). Nonparametric Statistical Tests. Chapman and Hall/CRC. doi:10.1201/b11427. ISBN 9781439867037.
  3. Kössler, W. (Wolfgang) (2006). Asymptotic power and efficiency of lepage-type tests for the treatment of combined location-scale alternatives. Humboldt-Universität zu Berlin. doi:10.18452/2462. hdl:18452/3114. OCLC 243600853.
  4. Mukherjee, Amitava; Marozzi, Marco (2019-08-01). "A class of percentile modified Lepage-type tests". Metrika. 82 (6): 657–689. doi:10.1007/s00184-018-0700-1. ISSN 1435-926X.
  5. Cucconi, Odoardo (1968). "Un Nuovo Test non Parametrico per Il Confronto Fra Due Gruppi di Valori Campionari". Giornale Degli Economisti e Annali di Economia. 27 (3/4): 225–248. JSTOR 23241361.
  6. Schneider, Grant; Chicken, Eric; Becvarik, Rachel (2018-05-16), NSM3: Functions and Datasets to Accompany Hollander, Wolfe, and Chicken – Nonparametric Statistical Methods, Third Edition, retrieved 2019-09-17
  7. Schulz, Andreas. "R Programme for Lepage Test" (PDF).
  8. Mukherjee, A.; Chakraborti, S. (2011-09-26). "A Distribution-free Control Chart for the Joint Monitoring of Location and Scale". Quality and Reliability Engineering International. 28 (3): 335–352. doi:10.1002/qre.1249. ISSN 0748-8017.
  9. Chowdhury, Shovan; Mukherjee, Amitava; Chakraborti, Subhabrata (2014-11-07). "Distribution-free Phase II CUSUM Control Chart for Joint Monitoring of Location and Scale" (PDF). Quality and Reliability Engineering International. 31 (1): 135–151. doi:10.1002/qre.1677. hdl:2263/50153. ISSN 0748-8017.
  10. Mukherjee, Amitava (2017-02-18). "Distribution-free phase-II exponentially weighted moving average schemes for joint monitoring of location and scale based on subgroup samples". The International Journal of Advanced Manufacturing Technology. 92 (1–4): 101–116. doi:10.1007/s00170-016-9977-2. ISSN 0268-3768.
  11. Mukherjee, Amitava; Marozzi, Marco (2016-05-17). "Distribution-free Lepage Type Circular-grid Charts for Joint Monitoring of Location and Scale Parameters of a Process". Quality and Reliability Engineering International. 33 (2): 241–274. doi:10.1002/qre.2002. ISSN 0748-8017.
  12. Rublík, František (2005). "The multisample version of the Lepage test". Kybernetika. 41 (6): [713]–733. hdl:10338.dmlcz/135688. ISSN 0023-5954.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.