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Vol. 15 No. 2 (2024)
Vol. 15 Núm. 2 (2024): Vol 15, Núm.2 (2024): Julio-Diciembre

Artículos de investigación / Research papers

Bootstrap versus Jackknife: Confidence intervals, hypothesis testing, density estimation, and kernel regression

https://doi.org/10.19053/01217488.v15.n2.2024.15900

Published 2024-10-10

  • Laura Cruz
    • ,
  • Jessica Blanco
    • ,
  • Ramón Giraldo

Laura Cruz
Universidad Nacional de Colombia image/svg+xml

Jessica Blanco
Universidad Nacional de Colombia image/svg+xml

Ramón Giraldo
a:1:{s:5:"es_ES";s:46:"Universidad Nacional de Colombia, Sede Bogotá";}

Abstract

Bootstrap and Jackknife methods are compared in various statistical contexts. Initially, these are evaluated using estimates of coefficients of variation obtained from samples of different probability models (Normal, Gamma, Binomial, and Poisson) generated by Monte Carlo simulation. With the results, the bias and variance of the estimators are evaluated. The performance of the two inferential procedures considered in one-sample problems, density estimation, and kernel regression, is also studied. The results show that in the case of the Jackknife coefficient of variation, it has a lower bias but a higher standard error. Bootstrap is a more powerful estimator in this context. Both methodologies produce similar results regarding density estimation (histogram and kernel). In regression Kernel, it is observed that Jackknife allows obtaining estimates of the regression bandwidth closer to the classical ones than those found with Bootstrap. The corresponding confidence intervals with Jackknife are shorter than those established with Bootstrap.

Keywords

Bootstrap, confidence intervals, Jackknife, kernel regression, local regression, power of the test

References

  1. Behme, A. Theory of Stochastic Objects: Probability, Stochastic Processes and Inference. Chapman &
  2. Hall/CRC Press, 2018
  3. Bonamente, M. Monte Carlo and Re-sampling Methods. In Statistics and Analysis of Scientific Data
  4. (pp. 351-367). Singapore: Springer Nature Singapore, 2022.
  5. Bose, A., Chatterjee, S. Comparison of bootstrap and jackknife variance estimators in linear regression:
  6. Second order results. Statistica Sinica. 2002, 575-598.
  7. Bowman, A., Azzalini, A. Applied smoothing techniques for data analysis: the kernel approach with
  8. S-Plus illustrations. OUP Oxford, 1973.
  9. Buckland, S. Monte Carlo confidence intervals. Biometrics. 1984; 811-817.
  10. Chen, Y. A tutorial on kernel density estimation and recent advances. Biostatistics & Epidemiology.
  11. ; 1(1), 161-187.
  12. DiCiccio, T., Efron, B. Bootstrap confidence intervals. Statistical Science. 1996; 11(3): 189-228.
  13. Donegani, M. Bootstrap adaptive test for two way analysis of variance. Biometrical Journal. 1992;
  14. (2): 141-146
  15. Donnelly-Makowecki, L., Moore, R. Hierarchical testing of three rainfall-runoff models in small
  16. forested catchments. Journal of Hydrology. 1999; 219(3-4): 136-152.
  17. Efron, B., Stein, C. The Jackknife estimate of variance. The Annals of Statistics. 1981; 586-596.
  18. Efron B., Tibshirani R. An introduction to the bootstrap. 1994; CRC Press.
  19. Freedman D., Peters S. Bootstrapping a regression equation: Some empirical results. Journal of Statistical
  20. Software. 2008; 25(7):1-37.
  21. Garay, A., Hashimoto, E., Ortega, E., Lachos, V. On estimation and influence diagnostics for zeroinflated
  22. negative binomial regression models. Computational Statistics & Data Analysis, 2011; 55(3):
  23. -1318.
  24. Gillibrand E., Jamieson A., Bagley, P., Zuur, A., Priede, I. Seasonal development of a deep pelagic
  25. bioluminescent layer in the temperate NE Atlantic Ocean. Marine Ecology Progress Series, 2007, 341:
  26. -43.
  27. Gong, G. Cross-validation, the jackknife, and the bootstrap: Excess error estimation in forward logistic
  28. regression. Journal of the American Statistical Association. 1986; 81 (393): 108-113.
  29. Hahn, J. Bootstrapping quantile regression estimators. Econometric Theory. 1995; 11(1): 105-121.
  30. Han, J., Li, G., Liu, H., Hu, H., Zhang, X. Stimulation of bioluminescence in Noctiluca sp. using
  31. controlled temperature changes. Luminescence. 2013; 28(5): 742-744.
  32. Heger, A., Ieno, E., King, N., Morris, K., Bagley, P., Priede, I. Deep-sea pelagic bioluminescence over
  33. the Mid-Atlantic Ridge. Deep Sea Research Part II: Topical Studies in Oceanography. 2008, 55(1-2),
  34. -136.
  35. Kohler, M., Schindler, A., Sperlich, S. 2014. A review and comparison of bandwidth selection methods
  36. for kernel regression. International Statistical Review. 2014; 82(2): 243-274.
  37. Lu, X., Su, L. Jackknife model averaging for quantile regressions. Journal of Econometrics. 2015;
  38. (1): 40-58.
  39. McCabe, P., Korb, O., Cole, J. Kernel density estimation applied to bond length, bond angle, and torsion
  40. angle distributions. Journal of Chemical Information and Modeling, 2014, 54(5): 1284-1288.
  41. Moulton, L., Zeger, S. Bootstrapping generalized linear models. Computational Statistics & Data
  42. Analysis. 1991; 11: 53-63.
  43. O´Brien, S., Webb, A., Brewer, M., Reid, J. Use of kernel density estimation and maximum curvature
  44. to set marine protected area boundaries: Identifying a special protection area for wintering red-throated
  45. divers in the UK. Biological Conservation. 2012, 156: 15-21.
  46. Oyeyemi, G. Comparison of bootstrap and jackknife methods of resampling in estimating popultion
  47. parameters. Global Journal of Pure and Applied Sciences. 2008; 1(2):217-220.
  48. Quenouille, M. Approximate test of correlation in time series. Journal of the Royal Statistical Society,
  49. Series B. 1949; 11:68-84
  50. Quenouille, M. Notes on bias in estimation. Biometrika. 1956; 43(3): 353-360.
  51. R Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical
  52. Computing. https://www.R-project.org/. 2022.
  53. Roda, A., Pasini, P., Mirasoli, M., Michelini, E., Guardigli, M. Biotechnological applications of
  54. bioluminescence and chemiluminescence. TRENDS in Biotechnology. 2004, 22(6), 295-303.
  55. Rudemo, M. Empirical choice of histograms and kernel density estimators. Scandinavian Journal of
  56. Statistics. 1982, 65-78.
  57. Scott, D. Histogram. Wiley Interdisciplinary Reviews: Computational Statistics. 2010, 2(1): 44-48.
  58. Sherman, M., Cessie, S. A comparison between bootstrap methods and generalized estimating equations
  59. for correlated outcomes in generalized linear models. Communications in Statistics-Simulation and
  60. Computation. 1997; 26(3): 901-925.
  61. Tukey, J. Bias and confidence in not quite large samples. Ann. Math. Statist. 1958; 29: 614.
  62. Widder, E. Marine bioluminescence. Why do so many animals in the open ocean make light?. Science.
  63. ; 328: 704-708.
  64. Wu, C. Jackknife, Bootstrap and other resampling methods in regression analysis. The Annals of
  65. Statistics. 1986; 14(4): 1261-1295.
  66. Zambom, A., Dias, R. A review of kernel density estimation with applications to econometrics. International
  67. Econometric Review. 2013; 5(1): 20-42.
  68. Zuur, A., Ieno, E. Smith, G. Analysing ecological data. Springer; 2007.
  69. Zuur, A. Additive mixed modelling applied on deep-sea pelagic bioluminescent organisms. In Mixed
  70. effects models and extensions in ecology with R. 2009; 399-422.

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