Bootstrap error-adjusted single-sample technique

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In statistics, the bootstrap error-adjusted single-sample technique (BEST or the BEAST) is a non-parametric method that is intended to allow an assessment to be made of the validity of a single sample. It is based on estimating a probability distribution representing what can be expected from valid samples.[1] This is done use a statistical method called bootstrapping, applied to previous samples that are known to be valid.


BEST provides advantages over other methods such as the Mahalanobis metric, because it does not assume that for all spectral groups have equal covariances [clarification needed] or that each group is drawn for a normally distributed population.[2] A quantitative approach involves BEST along with a nonparametric cluster analysis algorithm. Multidimensional standard deviations[clarification needed] (MDSs) between clusters and spectral[clarification needed] data points are calculated, where BEST considers each frequency to be taken from a separate dimension.[clarification needed][3]

BEST is based on a population, P, relative to some hyperspace, R, that represents the universe of possible samples. P* is the realized values of P based on a calibration set, T. T is used to find all possible variation in P. P* is bound by parameters C and B. C is the expectation value of P, written E(P), and B is a bootstrapping distribution called the Monte Carlo approximation. The standard deviation can be found using this technique. The values of B projected into hyperspace give rise to X. The hyperline from C to X gives rise to the skew adjusted standard deviation which is calculated in both directions of the hyperline.[4]


BEST is used in detection of sample tampering in pharmaceutical products. Valid (unaltered) samples are defined as those that fall inside the cluster of training-set points when the BEST is trained with unaltered product samples. False (tampered) samples are those that fall outside of the same cluster.[1]

Methods such as ICP-AES require capsules[clarification needed] to be emptied for analysis. A nondestructive method is valuable. A method such as NIRA[clarification needed] can be coupled to the BEST method in the following ways.[1]

  • Detect any tampered product by determining that it is not similar to the previously analyzed unaltered product.
  • Quantitatively identify the contaminant from a library of known adulterants in that product.
  • Provide quantitative indication of the amount of contaminant present.


  1. ^ a b c Lodder, Robert A.; Selby, Mark.; Hieftje, Gary M. (1987). "Detection of capsule tampering by near-infrared reflectance analysis". Analytical Chemistry 59: 1921–1930. doi:10.1021/ac00142a008.  edit
  2. ^ Efron, B.; Gong, G. (1983). "A Leisurely Look at the Bootstrap, the Jackknife, and Cross-Validation". The American Statistician 37 (1): 36–48. doi:10.2307/2685844.  edit
  3. ^ Joseph Mendendorp and Robert A. Lodder (2006) "Acoustic-Resonance Spectrometry as a Process Analytical Technology for Rapid and Accurate Tablet Identification" AAPS PharmSciTech, 7 (1) Article 25.
  4. ^ Sara J. Hamilton and Robert Lodder, "Hyperspectral Imaging Technology for Pharmaceutical Analysis", Society of Photo-Optical Instrumentation Engineers[full citation needed]

Further reading[edit]

  • Lodder, R.; Hieftje, G. (1988). "Quantile BEAST Attacks the False-Sample Problem in Near-Infrared Reflectance Analysis". Applied Spectroscopy 42 (8): 1351–1365. doi:10.1366/0003702884429652. 
  • Y. Zou, Robert A. Lodder (1993) "An Investigation of the Performance of the Extended Quantile BEAST in High Dimensional Hyperspace", paper #885 at the Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Atlanta, GA
  • Y. Zou, Robert A. Lodder (1993) "The Effect of Different Data Distributions on the Performance of the Extended Quantile BEAST in Pattern Recognition", paper #593 at the Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Atlanta, GA