Modeling mining deposit properties using multivariate multiple (A,U,Θ) estimators
Keywords:
mathematical modeling, mining deposits, estimator (A,U,Θ), multivariate estimator, effewctive estimator, feasible estimator, multiple estimator, estimation errorAbstract
This paper describes a procedure to estimate at a point of coordinates Pe, the value Z7e of a dependent variable Z7 that quantifies the spatial behavior of a property of a mineral deposit (for example, the volumetric mass), simultaneously using information from two databases named respectively BD1 and BD2. The procedure is based on the use of a Multiple Multivariate Estimator that, applied exhaustively to the combinations that are established for the possible values of the parameters (p, s and m) of a UPD kernel function, allows obtaining optimal results with respect to a coefficient of variation CVe which evaluates the relationship between the estimation error and the estimated value. The form in which the multiple multivariate estimator presented has been defined allows it to be classified as viable and effective.Downloads
References
Arlot, S. y Celisse, A. (2010). A survey of cross-validation procedures for model selection. Statistics Surveys, 4, 40-79. DOI: 10.1214/09-SS054
Arzola, José (2000). Sistemas de Ingeniería. Editorial Félix Varela, La Habana, Cuba. ISBN: 978-959-07-1762-8, DOI: 10.13140/RG.2.1. 2349.4249
Blum, A. & Oli, R. A. (2003). Metaheuristics in combinatorial optimization: Overview and conceptual comparison. ACM Computing Surveys, 35(3), 268–308. Disponible en: http://kurs info.himolde.no/forskningsgrupper/optimering/phdkurs/Metaheuristics%20in%20Combinatorial%20Optimization.pdf
Ding, Jie; Tarokh, Vahid & Yang, Yuhong (2018). Model Selection Techniques - An Overview. IEEE Signal Processing Magazine, 1-21. DOI: 10.1109/MSP.2018.2867638. Disponible en: https://arxiv.org /pdf/1810.09583.pdf
Legrá-Lobaina, A. A. (2015). Método UPD-L para estimar valores de una variable geominera medidos en un conjunto de puntos de Rn. Minería y Geología, 31(1), 1-12.
Legrá-Lobaina, A. A. (2017). Modelos de malla basados en estimadores (A,U,Θ). Revista HOLOS, 33(4), 88-110. DOI: 10.15628/holos. 2017.5351.
Legrá-Lobaina, A. A. (2018). Evaluación del error en estimaciones (A,U,Θ). Revista HOLOS, 34(3), 1-23. DOI: 10.15628/holos. 2018.6193.
Legrá-Lobaina, A. A. y Terrero-Matos, E. (2019). Modelación de variables eólicas mediante estimadores (A,U,Θ) multivariados. Minería y Geología, 35(1), 84-99. ISSN 1993 8012.
Legrá-Lobaina, A. A. (2020). Sensibilidad de los estimadores (A,U,Θ). Revista HOLOS, 36(1), 1-18. DOI: 10.15628/holos.2020.7282.
Legrá-Lobaina, A. A. (2022). Elementos teóricos y prácticos de la investigación científico-tecnológica. Primera Edición Digital, Editorial Félix Varela, ISBN: 978-959-07-2494-7. Disponible en: http://bibliografía.eduniv.cu:8083/
Miller, I.; Freund, J. y Johnson, R. (2005). Probabilidades y Estadísticas para ingenieros. Vol. I y II. 4ta ed. México: Prentice-Hall Hispanoamericana S. A. 624 p. ISBN: 0-13-712-761-8.
Peng, H.; Ozaqui, T.; Haggan-Ozaqui, V. y Toyoda, Y. (2003). A parameter optimization method for radial basis function type models. IEEE Trans Neural Netw., 14(2), 432-440. Disponible en: http://dx.doi.org/10.1109/TNN.2003.809395
Rivera, Sergio. (2004). Estado del Arte en la Ubicación Óptima de Capacitores y Estudio de Optimalidad de la Solución mediante Búsqueda Exhaustiva. Revista Ingeniería e Investigación, 56, 67–72. Disponible en: https://www.researchgate.net/publication/ 259074530_Estado_del_Arte_en_la_Ubicacion_Optima_de_Capacitores_y_Estudio_de_Optimalidad_de_la_Solucion_mediante_Busqueda_Exhaustiva
Tibshirani, Ryan (2013). Model selection and validation 1: Cross-validation. Data Mining, 36, 1-26. Disponible en: https:// www.stat.cmu.edu/~ryantibs/datamining/lectures/18-val1.pdf
Tomás Antonio, Justino; Polanco Almanza, Ramón G. y Legrá-Lobaina, A. A. (2020). Modelación 3D de la masa volumétrica mediante estimadores (A,U,Θ). Minería y Geología, 36(3), 300-315.
Vidal, V; Wolf, C & Dupont, F. (2012). Combinatorial mesh optimization. The Visual Computer, 28(5), 511-525. Disponible en: http://liris.cnrs.fr/Documents/Liris-5258.pdf
Zhang, Y. & Yang, Y. (2015). Cross-Validation for Selecting a Model Selection Procedure. Journal of Econometrics, 187, 95-112. Disponible en: http://users.stat.umn.edu/~yangx374/papers/AC V_v30.pdf
Published
How to Cite
Issue
Section
Copyright (c) 2025 Arístides Alejandro Legrá-Lobaina, Ramón Eddie Peña-Abreu, Eduardo Terrero- Matos, Ramón Gilberto Polanco-Almanza, Justino Tomás-António

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
- Authors retain copyright and guaranteeing the right magazine to be the first publication of the work as licensed under a Creative Commons Attribution-NonCommercial that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors may establish separate supplemental agreements for the exclusive distribution version of the work published in the journal (eg, place it in an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are allowed and recommended to disseminate their work through the Internet (e.g., in institutional telematic archives or on their websites) before and during the submission process, which can produce interesting exchanges and increase citations of the published work. (See The effect of open access)