@unpublished{kurepository52,
     institution = {Keiser University Latin American Campus},
           title = {Polynomial Model Selection with Small Samples: Fitting, Generalization, and Cross-Validation in the Analysis of International Tourism in Nicaragua (2020-2024)},
            note = {Unpublished},
            type = {Discussion Paper},
       publisher = {Keiser University Latin American Campus, San Marcos, Nicaragua},
        abstract = {This study addresses model selection in data-scarce regimes using five annual observations of international tourism arrivals in Nicaragua (2020-2024). Four candidate
specifications (linear, quadratic, cubic, and exponential) are fitted and evaluated via leave-one-out cross-validation (LOOCV), the PRESS statistic, and the corrected AICc. The results demonstrate that R2 is a severely biased proxy for predictive performance when p/n{$\ge$}0.4. The cubic model (R2 = 0.971) exhibits an out-of-sample prediction error six times larger than that of the linear model (PRESS = 2.61 {$\times$}106
vs. 4.31 {$\times$}105) and yields physically impossible forecasts. All criteria converge on the linear model as the optimal specification. Projections for 2025-2030 with
95\% parametric bootstrap intervals are provided, together with a fully reproducible Python pipeline.

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Este estudio aborda la selecci{\'o}n de modelos en reg{\'i}menes con escasez de datos utilizando cinco observaciones anuales de llegadas de turistas internacionales a Nicaragua (2020-2024). Se ajustan cuatro especificaciones candidatas (lineal, cuadr{\'a}tica, c{\'u}bica y exponencial) y se eval{\'u}an mediante validaci{\'o}n cruzada de exclusi{\'o}n de un elemento (LOOCV), el estad{\'i}stico PRESS y el AICc corregido. Los resultados demuestran que el R2 es un indicador sesgado del rendimiento predictivo cuando p/n {$\ge$} 0,4. El modelo c{\'u}bico (R2 = 0,971) presenta un error de predicci{\'o}n fuera de muestra seis veces mayor que el del modelo lineal (PRESS = 2,61 {$\times$} 10{$^6$} frente a 4,31 {$\times$} 10{$^5$}) y genera pron{\'o}sticos f{\'i}sicamente imposibles. Todos los criterios convergen en el modelo lineal como la especificaci{\'o}n {\'o}ptima. Se proporcionan proyecciones para el periodo 2025-2030 con intervalos de bootstrap param{\'e}tricos del 95 \%, junto con un flujo de trabajo en Python totalmente reproducible.},
             url = {https://kurepository.keiseruniversity.edu.ni/id/eprint/52/},
          author = {Silwany Garcia, Sara Samira},
        keywords = {Model selection; leave-one-out cross-validation; PRESS; corrected AIC; overfitting; tourism in Nicaragua; polynomial regression; statistical parsimony. Selecci{\'o}n de modelos; validaci{\'o}n cruzada de exclusi{\'o}n de un elemento; PRESS; AIC corregido; sobreajuste; turismo en Nicaragua; regresi{\'o}n polin{\'o}mica; parsimonia estad{\'i}stica.}
}