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2018 | 65 | z. 3 | 314--349
Tytuł artykułu

Nonparametric Versus Parametric Reasoning Based on Contingency Tables

Autorzy
Treść / Zawartość
Warianty tytułu
Wnioskowanie parametryczne i nieparametryczne w tablicach dwudzielczych i trójdzielczych
Języki publikacji
EN
Abstrakty
EN
This paper proposes scenarios of generating two-way and three way contingency tables (CTs). A concept of probability flow parameter (PFP) plays a crucial role in these scenarios. Additionally, measures of untruthfulness of H0 are defined. The power divergence statistics and the |X| statistics are used. This paper is a simple attempt to replace a nonparametric statistical inference from CTs by the parametric one. Maximum likelihood method is applied to estimate PFP and instructions of generating CTs according to scenarios in question are presented. The Monte Carlo method is used to carry out computer simulations. (original abstract)
W artykule proponowane są scenariusze generowania tablic dwudzielczych (TD) z parametrem przepływu prawdopodobieństwa i zdefiniowane są miary nieprawdziwości H0. W artykule wykorzystywane są statystyki z rodziny X2 oraz statystyka modułowa |X|. Niniejsza praca jest prostą próbą zastąpienia nieparametrycznej metody wnioskowania statystycznego metodą parametryczną. Metoda największej wiarygodności jest wykorzystana do oszacowania parametru przepływu prawdopodobieństwa. W pracy opisane są także instrukcje generowania TD za pomocą metody słupkowej. Symulacje komputerowe przeprowadzono metodami Monte Carlo. (abstrakt oryginalny)
Rocznik
Tom
65
Numer
Strony
314--349
Opis fizyczny
Twórcy
  • Pomeranian University in Słupsk
Bibliografia
  • Agresti A., (2002), Categorical Data Analysis, Wiley, New Jersey.
  • Allison P. D., Liker J. K., (1982), Analyzing Sequential Categorical Data on Dyadic Interaction: A Comment on Gottman.
  • Beh E. J., Davy P. J., (1998), Partitioning Pearson's Chi-squared Statistics for a Completely Ordered Three-Way Contingency Table, The Australian and New Zealand Journal of Statistics, 40, 465-477.
  • Bishop Y., Fienberg S., Holland, P., (1975), Discrete Multivariate Analysis - Theory and Practice, Cambridge, MA: MIT Press.
  • Blitzstein J., Diaconis P., (2011), A Sequential Importance Sampling Algorithm for Generating Random Graphs with Prescribed Degrees, Internet mathematics, 6 (4), 489-522.
  • Bock H. H., (2003), Two-Way Clustering for Contingency Tables: Maximizing A Dependence Measure, Between data science and applied data analysis, 143-154.
  • Chen Y., Diaconis P., Holmes S. P., Liu J.S., (2005), Sequential Monte Carlo Methods for Statistical Analysis of Tables, Journal of the American Statistical Association, 100 (469), 109-120.
  • Chen Y., Dinwoodie I. H., Sullivant S., (2006), Sequential Importance Sampling for Multiway Tables, The Annals of Statistics, 523-545.
  • Cressie N., Read T. R., (1984), Multinomial Goodness-Of-Fit Tests, Journal of the Royal Statistical Society, Series B (Methodological), 440-464.
  • Cryan M., Dyer M., (2003), A Polynomial-Time Algorithm to Approximately Count Contingency Tables When the Number of Rows Is Constant, Journal of Computer and System Sciences, 67 (2), 291-310.
  • Cryan M., Dyer M., Goldberg L. A., Jerrum M., Martin R., (2006), Rapidly Mixing Markov Chains for Sampling Contingency Tables with A Constant Number of Rows, SIAM Journal on Computing, 36 (1), 247-278.
  • Cung, B., (2013), Crime and Demographics: An Analysis of LAPD Crime Data. DeSalvo S., Zhao J. Y., (2015), Random Sampling of Contingency Tables Via Probabilistic Divide- And-Conquer. arXiv preprint arXiv:1507.00070.
  • Diaconis P., Sturmfels B., (1998), Algebraic Algorithms for Sampling from Conditional Distributions, The Annals of statistics, 26 (1), 363-397.
  • Dickhaus T., Straßburger K., Schunk D., Morcillo-Suarez C., Illig T., Navarro A., (2012), How to Analyze Many Contingency Tables Simultaneously in Genetic Association Studies, Statistical Applications in Genetics and Molecular Biology, 11 (4),12.
  • El Galta R., Stijnen T., Houwing-Duistermaat J. J., (2008), Testing for Genetic Association: A Powerful Score Test, Statistics in Medicine, 27 (22), 4596-4609.
  • Fishman G. S., (2012), Counting Contingency Tables Via Multistage Markov Chain Monte Carlo. Journal of Computational and Graphical Statistics, 21(3), 713-738.
  • Freeman M. F., Tukey J. W., (1950), Transformations Related to the Angular and the Square Root, Annals of Mathematical Statistics, 21, 607-611.
  • Gokhale D., Kullback S., (1978), The Information in Contingency Tables, Marcel Dekker, Inc., New York.
  • Goodman L., Kruskal W., (1954), Measures of Association for Cross Classifications, Journal of the American Statistical Association, 49, 732-764.
  • Gray L. N., Williams J. S., (1975), Goodman and Kruskal's Tau b: Multiple and Partial Analogs, In: Proceedings of the Social Statistics Section, Journal of the American Statistical Association, 444-448.
  • Haas P. J., Hueske F., Markl V., (2007), Detecting Attribute Dependencies from Query Feedback, Proceedings of the 33rd International Conference on Very Large Data Bases, VLDB Endowment, 830-841.
  • Harshman R. A., (1970), Foundations of the PARAFAC Procedure: Models and Conditions for an Explanatory Multi-modal Factor Analysis, UCLA Working Papers in Phonetics, 16, 1-84.
  • Ilyas I. F., Markl V., Haas P., Brown P., Aboulnaga A., (2004), CORDS: Automatic Discovery of Correlations and Soft Functional Dependencies, Proceedings of the 2004 ACM SIGMOD international conference on Management of data, ACM, 647-658.
  • Iossifova R., Marmolejo-Ramos F., (2013), When The Body Is Time: Spatial and Temporal Deixis in Children with Visual Impairments and Sighted Children, Research in Developmental Disabilities, 34 (7), 2173-2184.
  • Kaski S., Nikkila J., Sinkkonen J., Lahti L., Knuuttila J. E., Roos C., (2005), Associative Clustering for Exploring Dependencies Between Functional Genomics Data Sets, IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB), 2 (3), 203-216.
  • Kullback S., (1959), Information Theory and Statistics, Wiley, New York.
  • Lombardo R., (2011), Three-Way Association Measure Decompositions: The Delta index, Journal of Statistical Planning and Inference, 141, 1789-1799.
  • Lombardo R., Beh E. J., (2010), Simple and Multiple Correspondence Analysis for Ordinal-Scale Variables Using Orthogonal Polynomials, Journal of Applied Statistics, 37 (12), 2101-2116.
  • Marcotorchino F., (1984), Utilisation des Comparaisons par Pairesen Statistique des Contingences. Partie (I), Etude IBM F069, France.
  • Neyman J., (1949), Contribution to the Theory of the x2 Test, Proceedings of the First Berkeley Symposium on Mathematical Statistics and Probability, Univ. of Calif. Press, 239-273.
  • Oates T., Cohen P. R., (1996), Searching for Structure in Multiple Streams of Data, ICML 96.
  • Pardo M. C., (1996), An Empirical Investigation of Cressie and Read Tests for the Hypothesis of Independence in Three-way Contingency Tables, Kybernetika 32 (2), 175-183.
  • Pearson K., (1900), On the Criterion That a Given System of Deviations From the Probable in the Case of a Correlated System of Variables is Such That it Can be Reasonably Supposed to Have Arisen From Random Sampling, Philosophy Magazine Series, 50, 157-172.
  • Schrepp M., (2003), A Method for The Analysis of Hierarchical Dependencies Between Items of a Questionnaire, Methods of Psychological Research Online, 19, 43-79.
  • Sokal R. R., Rohlf F. J., (2012), Biometry: The Principles and Practice of Statistics in Biological Research, Freeman, New York.
  • Steinle M., Aberer. K, Girdzijauskas S., Lovis C., (2006), Mapping Moving Landscapes by Mining Mountains of Logs: Novel Techniques for Dependency Model Generation, Proceedings of the 32nd international conference on Very large data bases, VLDB Endowment, 1093-1102.
  • Sulewski P., (2009), Two-By-Two Contingency Table as a Goodness-Of-Fit Test, Computational Methods in Science and Technology, 15 (2), 203-211.
  • Sulewski P., (2013), Modyfikacja testu niezależności, Wiadomości Statystyczne, 10, 1-19.
  • Sulewski P., (2016), Moc testów niezależności w tablicy dwudzielczej większej niż 2x2, Przegląd Statystyczny, 63 (2), 191-209.
  • Sulewski P., (2018a), Power Analysis of Independence Testing for the Three-way Contingency Tables of Small Sizes, Journal of Applied Statistics, 45 (13), 2481-2498.
  • Sulewski P., (2018b), Nonparametric Versus Parametric Reasoning Based on 2×2 Contingency Tables, Computational Methods in Science and Technology, 24 (2), 143-153.
  • Sulewski P., Motyka R., (2015), Power Analysis of Independence Testing for Contingency Tables. Scientific Journal of Polish Naval Academy, 56, 37-46.
  • Tucker L. R., (1963), Implications of Factor Analysis of Three-Way Matrices for Measurement of Change. In Problems in Measuring Change, 122-137.
  • Van Belle G., Fisher L.D., Heagerty P. J., Lumley T., (2004), Categorical Data: Contingency Tables, John Wiley & Sons.
  • Yoshida R., Xi J., Wei S., Zhou F., Haws D., (2011), Semigroups and Sequential Importance Sampling for Multiway Tables. arXiv preprint arXiv:1111.6518.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171559525

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