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Two-way layout factorial experiments of spatial point pattern responses in mineral flotation

Author

Listed:
  • Jonatan A. González

    (University Jaume I)

  • Bernardo M. Lagos-Álvarez

    (University of Concepción)

  • Jorge Mateu

    (University Jaume I)

Abstract

Factorial experiments are well-understood when the given observations are outcomes of random variables. However, when we observe spatial point patterns in each combination of factors cells, the methodology is much less developed. Motivated by a real problem of locations of bubbles in a mineral flotation experiment where the interest is analysing if the spatial distribution might be affected by frother concentrations and volumetric airflow rates, we develop an approach for statistical testing of two-way factorial experiments for spatial point patterns. We describe the point patterns through the K-function, a second-order summary statistic, and develop a set of new Fisher-based statistics using weighted means. For inference by Monte Carlo, we use random permutations of weighted residuals depending on the null hypothesis. We conduct simulation experiments to demonstrate the performance of the new test statistics and present the results of the real problem.

Suggested Citation

  • Jonatan A. González & Bernardo M. Lagos-Álvarez & Jorge Mateu, 2021. "Two-way layout factorial experiments of spatial point pattern responses in mineral flotation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 1046-1075, December.
  • Handle: RePEc:spr:testjl:v:30:y:2021:i:4:d:10.1007_s11749-021-00768-w
    DOI: 10.1007/s11749-021-00768-w
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    References listed on IDEAS

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    1. Ferraty, Frederic & Vieu, Philippe & Viguier-Pla, Sylvie, 2007. "Factor-based comparison of groups of curves," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4903-4910, June.
    2. A. J. Baddeley & J. Møller & R. Waagepetersen, 2000. "Non‐ and semi‐parametric estimation of interaction in inhomogeneous point patterns," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 54(3), pages 329-350, November.
    3. Ute Hahn & Eva B. Vedel Jensen, 2016. "Hidden Second-order Stationary Spatial Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 455-475, June.
    4. Ute Hahn, 2012. "A Studentized Permutation Test for the Comparison of Spatial Point Patterns," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 754-764, June.
    5. Cuevas, Antonio & Febrero, Manuel & Fraiman, Ricardo, 2004. "An anova test for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 111-122, August.
    6. Tomasz Górecki & Łukasz Smaga, 2015. "A comparison of tests for the one-way ANOVA problem for functional data," Computational Statistics, Springer, vol. 30(4), pages 987-1010, December.
    7. M. N. M. van Lieshout & A. J. Baddeley, 1996. "A nonparametric measure of spatial interaction in point patterns," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 50(3), pages 344-361, November.
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    Cited by:

    1. Yuichi Goto & Koichi Arakaki & Yan Liu & Masanobu Taniguchi, 2023. "Homogeneity tests for one-way models with dependent errors under correlated groups," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 163-183, March.
    2. Yuichi Goto & Kotone Suzuki & Xiaofei Xu & Masanobu Taniguchi, 2023. "Tests for the existence of group effects and interactions for two-way models with dependent errors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(3), pages 511-532, June.

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