Análisis de la variabilidad y precisión en la estimación de intervalos de confianza en pruebas de hipótesis con desviaciones estándar variables: aplicación a datos de física de partículas del CERN y Zenodo.

The current research work ‘Analysis of variability and precision in the estimation of confidence intervals in hypothesis testing with variable standard deviations: application to particle physics jet data from CERN and Zenodo’, aims to comparatively evaluate the effectiveness of three non-parametric statistical methods in constructing confidence intervals for the sample standard deviation in the presence of heteroscedasticity. The research is based on the empirical variable transverse momentum of the jet (Jet_pt), derived from real experimental data from the CMS detector. The overall objective was to analyze the precision and efficiency of the intervals generated using three approaches: the logarithmic transformation of the chi-square interval, the empirical quantile method, and the percentile bootstrap. A comparative quantitative design with random subsampling and processing in R language was used, applying 113 subsamples per scenario. The results reveal that the logarithmic method has the shortest average interval length, while the bootstrap maintains an adequate balance between empirical coverage and width. The quantile approach, although robust in skewed distributions, showed greater dispersion under conditions of high variability. It is concluded that the logarithmic method offers the best inferential precision under heteroscedasticity, and that bootstrap is a flexible tool for non-normal distributions, thus validating the importance of the non-parametric approach in real scenarios of high statistical complexity.

• 1. Verfasser: Salazar Andrade, Andrés Eduardo (author)
• Format: masterThesis
• Sprache: spa
• Veröffentlicht: 2025
• Schlagworte: intervalos de confianza; desviación estándar; heterocedasticidad; métodos no paramétricos; submuestreo
• Online Zugang: http://dspace.unach.edu.ec/handle/51000/15775