IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v167y2022ics0167947321002139.html
   My bibliography  Save this article

The general goodness-of-fit tests for correlated data

Author

Listed:
  • Zhang, Hong
  • Wu, Zheyang

Abstract

Analyzing correlated data by goodness-of-fit type tests is a critical statistical problem in many applications. A unified framework is provided through a general family of goodness-of-fit tests (GGOF) to address this problem. The GGOF family covers many classic and newly developed tests, such as the minimal p-value test, Simes test, the GATES, one-sided Kolmogorov-Smirnov type tests, one-sided phi-divergence tests, the generalized Higher Criticism, the generalized Berk-Jones, etc. It is shown that the omnibus test that automatically adapts among GGOF statistics for given data, i.e., the GGOF-O, is still contained in the GGOF family and is computationally efficient. For analytically controlling the type I error rate of any GGOF tests, exact calculation is deduced under the Gaussian model with positive equal correlations. Based on that, the effective correlation coefficient (ECC) algorithm is proposed to address arbitrary correlations. Simulations are used to explore how signal and correlation patterns jointly influence typical GGOF tests' statistical power. The GGOF-O is shown robustly powerful across various signal and correlation patterns. As demonstrated by a study of bone mineral density, the GGOF framework has good potential for detecting novel disease genes in genetic summary data analysis. Computational tools are available in the R package SetTest on the CRAN.

Suggested Citation

  • Zhang, Hong & Wu, Zheyang, 2022. "The general goodness-of-fit tests for correlated data," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:csdana:v:167:y:2022:i:c:s0167947321002139
    DOI: 10.1016/j.csda.2021.107379
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947321002139
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2021.107379?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Rémy Chicheportiche & Jean-Philippe Bouchaud, 2011. "Goodness-of-Fit tests with Dependent Observations," Post-Print hal-00621061, HAL.
    2. Mariaelisa Graff & Robert A Scott & Anne E Justice & Kristin L Young & Mary F Feitosa & Llilda Barata & Thomas W Winkler & Audrey Y Chu & Anubha Mahajan & David Hadley & Luting Xue & Tsegaselassie Wor, 2017. "Genome-wide physical activity interactions in adiposity ― A meta-analysis of 200,452 adults," PLOS Genetics, Public Library of Science, vol. 13(4), pages 1-26, April.
    3. Ian Barnett & Rajarshi Mukherjee & Xihong Lin, 2017. "The Generalized Higher Criticism for Testing SNP-Set Effects in Genetic Association Studies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 64-76, January.
    4. David E. Reich & Michele Cargill & Stacey Bolk & James Ireland & Pardis C. Sabeti & Daniel J. Richter & Thomas Lavery & Rose Kouyoumjian & Shelli F. Farhadian & Ryk Ward & Eric S. Lander, 2001. "Linkage disequilibrium in the human genome," Nature, Nature, vol. 411(6834), pages 199-204, May.
    5. Remy Chicheportiche & Jean-Philippe Bouchaud, 2011. "Goodness-of-Fit tests with Dependent Observations," Papers 1106.3016, arXiv.org, revised Aug 2011.
    6. D. Y. Lin & D. Zeng, 2010. "On the relative efficiency of using summary statistics versus individual-level data in meta-analysis," Biometrika, Biometrika Trust, vol. 97(2), pages 321-332.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vance Martin & Yoshihiko Nishiyama & John Stachurski, 2011. "A Goodness of Fit Test for Ergodic Markov Processes," ANU Working Papers in Economics and Econometrics 2011-557, Australian National University, College of Business and Economics, School of Economics.
    2. Partida, Alberto & Gerassis, Saki & Criado, Regino & Romance, Miguel & Giráldez, Eduardo & Taboada, Javier, 2022. "The chaotic, self-similar and hierarchical patterns in Bitcoin and Ethereum price series," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    3. Michele Caraglio & Fulvio Baldovin & Attilio L. Stella, 2021. "How Fast Does the Clock of Finance Run?—A Time-Definition Enforcing Stationarity and Quantifying Overnight Duration," JRFM, MDPI, vol. 14(8), pages 1-15, August.
    4. Dangxing Chen, 2019. "Does the leverage effect affect the return distribution?," Papers 1909.08662, arXiv.org, revised Sep 2019.
    5. Morales, Raffaello & Di Matteo, T. & Gramatica, Ruggero & Aste, Tomaso, 2012. "Dynamical generalized Hurst exponent as a tool to monitor unstable periods in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3180-3189.
    6. Jean-Philippe Bouchaud, 2021. "Radical Complexity," Papers 2103.09692, arXiv.org.
    7. Alex D Washburne & Joshua W Burby & Daniel Lacker, 2016. "Novel Covariance-Based Neutrality Test of Time-Series Data Reveals Asymmetries in Ecological and Economic Systems," PLOS Computational Biology, Public Library of Science, vol. 12(9), pages 1-14, September.
    8. Hong Zhang & Zheyang Wu, 2023. "The generalized Fisher's combination and accurate p‐value calculation under dependence," Biometrics, The International Biometric Society, vol. 79(2), pages 1159-1172, June.
    9. Chicheportiche, Rémy & Chakraborti, Anirban, 2017. "A model-free characterization of recurrences in stationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 312-318.
    10. Jincheng Zhou & James S. Hodges & Haitao Chu, 2020. "Rejoinder to “CACE and meta‐analysis (letter to the editor)” by Stuart Baker," Biometrics, The International Biometric Society, vol. 76(4), pages 1385-1389, December.
    11. Pietro Biroli & Titus Galama & Stephanie von Hinke & Hans van Kippersluis & Kevin Thom, 2022. "Economics and Econometrics of Gene-Environment Interplay," Bristol Economics Discussion Papers 22/759, School of Economics, University of Bristol, UK.
    12. Nicole Deflaux & Margaret Sunitha Selvaraj & Henry Robert Condon & Kelsey Mayo & Sara Haidermota & Melissa A. Basford & Chris Lunt & Anthony A. Philippakis & Dan M. Roden & Joshua C. Denny & Anjene Mu, 2023. "Demonstrating paths for unlocking the value of cloud genomics through cross cohort analysis," Nature Communications, Nature, vol. 14(1), pages 1-10, December.
    13. Chung-Feng Kao & Jia-Rou Liu & Hung Hung & Po-Hsiu Kuo, 2015. "A Robust GWSS Method to Simultaneously Detect Rare and Common Variants for Complex Disease," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-14, April.
    14. Haipeng Li & Thomas Wiehe, 2013. "Coalescent Tree Imbalance and a Simple Test for Selective Sweeps Based on Microsatellite Variation," PLOS Computational Biology, Public Library of Science, vol. 9(5), pages 1-14, May.
    15. Shuxia Guo & Yunhua Hu & Yusong Ding & Jiaming Liu & Mei Zhang & Rulin Ma & Heng Guo & Kui Wang & Jia He & Yizhong Yan & Dongsheng Rui & Feng Sun & Lati Mu & Qiang Niu & Jingyu Zhang & Shugang Li, 2015. "Association between Eight Functional Polymorphisms and Haplotypes in the Cholesterol Ester Transfer Protein (CETP) Gene and Dyslipidemia in National Minority Adults in the Far West Region of China," IJERPH, MDPI, vol. 12(12), pages 1-14, December.
    16. Li Qin & Wu Rongling, 2009. "A Multilocus Model for Constructing a Linkage Disequilibrium Map in Human Populations," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-25, February.
    17. Shpak, Max & Ni, Yang & Lu, Jie & Müller, Peter, 2017. "Variance in estimated pairwise genetic distance under high versus low coverage sequencing: The contribution of linkage disequilibrium," Theoretical Population Biology, Elsevier, vol. 117(C), pages 51-63.
    18. Wei Zhao & Erin B. Ware & Zihuai He & Sharon L. R. Kardia & Jessica D. Faul & Jennifer A. Smith, 2017. "Interaction between Social/Psychosocial Factors and Genetic Variants on Body Mass Index: A Gene-Environment Interaction Analysis in a Longitudinal Setting," IJERPH, MDPI, vol. 14(10), pages 1-17, September.
    19. Hou, Wei & Liu, Tian & Li, Yao & Li, Qin & Li, Jiahan & Das, Kiranmoy & Berg, Arthur & Wu, Rongling, 2009. "Multilocus genomics of outcrossing plant populations," Theoretical Population Biology, Elsevier, vol. 76(1), pages 68-76.
    20. Xiaoshuai Zhang & Xiaowei Yang & Zhongshang Yuan & Yanxun Liu & Fangyu Li & Bin Peng & Dianwen Zhu & Jinghua Zhao & Fuzhong Xue, 2013. "A PLSPM-Based Test Statistic for Detecting Gene-Gene Co-Association in Genome-Wide Association Study with Case-Control Design," PLOS ONE, Public Library of Science, vol. 8(4), pages 1-8, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:167:y:2022:i:c:s0167947321002139. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.