IDEAS home Printed from https://ideas.repec.org/p/cte/wsrepe/35324.html
   My bibliography  Save this paper

Data-driven stabilizations of goodness-of-fit tests

Author

Listed:
  • Fernández de Marcos Giménez de los Galanes, Alberto

Abstract

Exact null distributions of goodness-of-fit test statistics are generally challenging to obtain in tractable forms. Practitioners are therefore usually obliged to rely on asymptotic null distributions or Monte Carlo methods, either in the form of a lookup table or carried out on demand, to apply a goodness-of-fit test. Stephens (1970) provided remarkable simple and useful transformations of several classic goodness-of-fit test statistics that stabilized their exact-n critical values for varying sample sizes n. However, detail on the accuracy of these and subsequent transformations in yielding exact p-values, or even deep understanding on the derivation of several transformations, is still scarce nowadays. We illuminate and automatize, using modern tools, the latter stabilization approach to (i) expand its scope of applicability and (ii) yield semi-continuous exact p-values, as opposed to exact critical values for fixed significance levels. We show improvements on the stabilization accuracy of the exact null distributions of the Kolmogorov-Smirnov, Cramér-von Mises, Anderson-Darling, Kuiper, and Watson test statistics. In addition, we provide a parameter-dependent exact-n stabilization for several novel statistics for testing uniformity on the hypersphere of arbitrary dimension. A data application in astronomy illustrates the benefits of the advocated stabilization for quickly analyzing small-to-moderate sequentially-measured samples.

Suggested Citation

  • Fernández de Marcos Giménez de los Galanes, Alberto, 2022. "Data-driven stabilizations of goodness-of-fit tests," DES - Working Papers. Statistics and Econometrics. WS 35324, Universidad Carlos III de Madrid. Departamento de Estadística.
  • Handle: RePEc:cte:wsrepe:35324
    as

    Download full text from publisher

    File URL: https://e-archivo.uc3m.es/rest/api/core/bitstreams/aa90c0fb-5ec9-435a-ac6b-e24dc71a9829/content
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Neil Marks, 2007. "Kolmogorov-Smirnov Test Statistic and Critical Values for the Erlang-3 and Erlang-4 Distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(8), pages 899-906.
    2. Marco Di Marzio & Agnese Panzera & Charles C. Taylor, 2012. "Smooth estimation of circular cumulative distribution functions and quantiles," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 935-949, December.
    3. Arthur Pewsey & Eduardo García-Portugués, 2021. "Rejoinder on: Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 76-82, March.
    4. Marsaglia, George & Tsang, Wai Wan & Wang, Jingbo, 2003. "Evaluating Kolmogorov's Distribution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 8(i18).
    5. Marsaglia, George & Marsaglia, John, 2004. "Evaluating the Anderson-Darling Distribution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 9(i02).
    6. García-Portugués, Eduardo & Crujeiras, Rosa M. & González-Manteiga, Wenceslao, 2013. "Kernel density estimation for directional–linear data," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 152-175.
    7. A. N. Pettitt, 1977. "Testing the Normality of Several Independent Samples Using the Anderson‐Darling Statistic," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(2), pages 156-161, June.
    8. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    9. Brown, J. Randall & Harvey, Milton E., 2007. "Rational Arithmetic Mathematica Functions to Evaluate the One-sided One-sample K-S Cumulative Sample Distribution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 19(i06).
    10. Jupp, P.E. & Kume, A., 2020. "Measures of goodness of fit obtained by almost-canonical transformations on Riemannian manifolds," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
    11. K. V. Mardia, 1999. "Directional statistics and shape analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 949-957.
    12. Y. A. S. Hegazy & J. R. Green, 1975. "Some New Goodness‐Of‐Fit Tests Using Order Statistics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 24(3), pages 299-308, November.
    13. Eddelbuettel, Dirk & Francois, Romain, 2011. "Rcpp: Seamless R and C++ Integration," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i08).
    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. Fernández-de-Marcos, Alberto & García-Portugués, Eduardo, 2023. "Data-driven stabilizations of goodness-of-fit tests," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    2. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    3. Jeon, Jeong Min & Van Keilegom, Ingrid, 2023. "Density estimation for mixed Euclidean and non-Euclidean data in the presence of measurement error," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    4. Mardia, Kanti V. & Wiechers, Henrik & Eltzner, Benjamin & Huckemann, Stephan F., 2022. "Principal component analysis and clustering on manifolds," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    5. Andrew Harvey & Dario Palumbo, 2023. "Regime switching models for circular and linear time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(4), pages 374-392, July.
    6. Shogo Kato & Arthur Pewsey & M. C. Jones, 2022. "Tractable circula densities from Fourier series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 595-618, September.
    7. William Bell & Saralees Nadarajah, 2024. "A Review of Wrapped Distributions for Circular Data," Mathematics, MDPI, vol. 12(16), pages 1-51, August.
    8. Andrade, Ana C.C. & Pereira, Gustavo H.A. & Artes, Rinaldo, 2023. "The circular quantile residual," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    9. Kim, Young Shin & Lee, Jaesung & Mittnik, Stefan & Park, Jiho, 2015. "Quanto option pricing in the presence of fat tails and asymmetric dependence," Journal of Econometrics, Elsevier, vol. 187(2), pages 512-520.
    10. Kanti V. Mardia & Karthik Sriram, 2023. "Families of Discrete Circular Distributions with Some Novel Applications," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 1-42, February.
    11. Sloot Henrik, 2022. "Implementing Markovian models for extendible Marshall–Olkin distributions," Dependence Modeling, De Gruyter, vol. 10(1), pages 308-343, January.
    12. Harvey, Andrew & Hurn, Stan & Palumbo, Dario & Thiele, Stephen, 2024. "Modelling circular time series," Journal of Econometrics, Elsevier, vol. 239(1).
    13. BenSaïda, Ahmed & Slim, Skander, 2016. "Highly flexible distributions to fit multiple frequency financial returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 203-213.
    14. Cindy Frascolla & Guillaume Lecuelle & Pascal Schlich & Hervé Cardot, 2022. "Two sample tests for Semi-Markov processes with parametric sojourn time distributions: an application in sensory analysis," Computational Statistics, Springer, vol. 37(5), pages 2553-2580, November.
    15. Tatjana Miljkovic & Saleem Shaik & Dragan Miljkovic, 2017. "Redefining standards for body mass index of the US population based on BRFSS data using mixtures," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(2), pages 197-211, January.
    16. Samrachana Adhikari & Tracy Sweet & Brian Junker, 2021. "Analysis of longitudinal advice‐seeking networks following implementation of high stakes testing," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(4), pages 1475-1500, October.
    17. Paula Saavedra-Nieves & Rosa M. Crujeiras, 2022. "Nonparametric estimation of directional highest density regions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(3), pages 761-796, September.
    18. Bill Venables, 2017. "JOHN M. CHAMBERS . Extending R . Boca Raton : CRC Press," Biometrics, The International Biometric Society, vol. 73(2), pages 709-710, June.
    19. Anthony Medford & James W. Vaupel, 2020. "Extremes are not normal: a reminder to demographers," Journal of Population Research, Springer, vol. 37(1), pages 91-106, March.
    20. Abe, Toshihiro & Miyata, Yoichi & Shiohama, Takayuki, 2023. "Bayesian estimation for mode and anti-mode preserving circular distributions," Econometrics and Statistics, Elsevier, vol. 27(C), pages 136-160.

    More about this item

    Keywords

    Exact Distribution;

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:cte:wsrepe:35324. 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: Ana Poveda (email available below). General contact details of provider: http://portal.uc3m.es/portal/page/portal/dpto_estadistica .

    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.