A Generalized Bootstrap Technique for Dependent Observations


  • Roberto N. Padua
  • Mark S. Borres University of San Jose-Recoletos
  • Randy K. Salazar University of San Jose-Recoletos




bootstrap, dependent observations, subspace, Cholesky’s method, LU-Decomposition


The bootstrap method for re-sampling essentially obtains the re-sampled observations from the empirical distribution function of the original data. The method relies heavily on the assumption of independence of the observations (iid). When the original data are correlated, then the usual bootstrap technique may fail to give appropriate re-sampled data. The present study proposes a new method for generating bootstrap observations from dependent observations knowing the original correlation structure of the data. Independent and identically distributed initial bootstrap samples are obtained from the
empirical cumulative distribution function of the data. The bootstrap re-samples from the original data are obtained from the space generated by the initial bootstrap subsamples. It is shown that the correlation structure of the bootstrap samples obtained is the same as the original data. Simulations show that the relative error and the mean-squared error decrease with increasing sample size. However, both types of error increase with increasing dimensionality of a multivariate normal distribution.

Author Biographies

Roberto N. Padua

Dr. Roberto Natividad Padua, scientist, received his PhD in Mathematical Statistics from Clemson University, South Carolina, USA under the Fullbright-Hays scholarship grant. He is an accomplished author, a multi-awarded researcher and an internationally acclaimed lecturer. Dr. Padua is a former Commissioner of CHED and currently a consultant to several state and private universities. He is also conducting lectures on research and Fractal Statistics. Dr. Padua is a Summa Cum Laude, BS in Mathematics Teaching graduate from the Philippine Normal College under the National Science Development Board (NSDB) program. He obtained his MS in Mathematics Education Degree from the Centro Escolar University as a Presidential Scholar.

Mark S. Borres, University of San Jose-Recoletos

graduated Bachelor of Science in Mathematics–major in Pure Mathematics at the University of the Philippines, Cebu College. Since 2009, he worked for the University of San Jose- Recoletos as a faculty member of the College of Arts and Sciences and handled Mathematics subjects such as College Algebra, Advanced Algebra, Abstract Algebra, Analytical Geometry, Euclidean geometry, Trigonometry, Business Mathematics, Linear Programming, Mathematics of Investment, Discrete Structure, and Statistics across colleges.

Randy K. Salazar, University of San Jose-Recoletos

is a Mechanical Engineer, Assistant Professor of the University of San Jose Recoletos teaching Mechanical Engineering. Holder of a Masters in Science in Management Engineering from the University of San Jose Recoletos and finishing his Masters degree in Mechanical Engineering – Dynamic Design Systems at the University of San Carlos.


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Lomangaya, Wilma. Sampling from a Univariate Time Series. (Unpublished Doctoral Dissertation, 2010, University of Rizal System)




How to Cite

Padua, R. N., Borres, M. S., & Salazar, R. K. (2014). A Generalized Bootstrap Technique for Dependent Observations. Recoletos Multidisciplinary Research Journal, 2(1). https://doi.org/10.32871/rmrj1402.01.05




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