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.

## Methodology

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]

## Application

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.

## References

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.
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.
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]