The bootstrap: a tutorial

Abstract Bootstrap methods have gained wide acceptance and huge popularity in the field of applied statistics. The bootstrap is able to provide accurate answers in cases where other methods are simply not available, or where the usual approximations are invalid. The number of applications in chemistry, however, has been rather limited. One possible cause for this is the overwhelming number of techniques available. This tutorial aims to introduce the basic concepts of bootstrap methods, provide some guidance as to what bootstrap methods are appropriate in different situations, and illustrate several potential application areas in chemometrics by worked examples.

[1]  B. Efron.  Bootstrap Methods: Another Look at the Jackknife , 1979 .

[2]  R. Lodder,et al.  Detection of Subpopulations in Near-Infrared Reflectance Analysis , 1988 .

[3]  G. A. Young,et al.  Bootstrap: More than a Stab in the Dark? , 1994 .

[4]  Robert Tibshirani,et al.  An Introduction to the Bootstrap , 1994 .

[5]  Hein Putter,et al.  Empirical Edgeworth expansions for symmetric statistics , 1998 .

[6]  Binne Zwanenburg,et al.  Clathrate‐Type Complexation of Cephalosporins with β‐Naphthol , 1999 .

[7]  Hilko van der Voet,et al.  Comparing the predictive accuracy of models using a simple randomization test , 1994 .

[8]  Mark T. D. Cronin,et al.  Embedded Cluster Modelling - a Novel Method for Analysing Embedded Data Sets. , 1999 .

[9]  M. Stone.  Cross‐Validatory Choice and Assessment of Statistical Predictions , 1976 .

[10]  Kevin J. Coakley,et al.  Detection and quantification of isotopic ratio inhomogeneity , 1998 .

[11]  J. Chambers,et al.  The New S Language , 1989 .

[12]  Lutgarde M. C. Buydens,et al.  Molecular challenges in modern chemometrics , 1999 .

[13]  B. Efron.  Jackknife‐After‐Bootstrap Standard Errors and Influence Functions , 1992 .

[14]  L.M.C. Buydens,et al.  Aspects of network training and validation on noisy data: Part 2. Validation aspects , 1998 .

[15]  D. W. Osten,et al.  Selection of optimal regression models via cross‐validation , 1988 .

[16]  D. Massart,et al.  Elimination of uninformative variables for multivariate calibration. , 1996, Analytical chemistry.

[17]  Stuart L. Crawford.  Extensions to the CART Algorithm , 1989, Int. J. Man Mach. Stud..

[18]  H. Putter,et al.  Resampling: Consistency of Substitution Estimators , 1996 .

[19]  Luis A. Sarabia,et al.  Using continuum regression for quantitative analysis with overlapping signals obtained by differential pulse polarography , 1996 .

[20]  R. Wehrens,et al.  Bootstrapping principal component regression models , 1997 .

[21]  Tapon Roy,et al.  Bootstrap accuracy for non‐linear regression models , 1994 .

[22]  Anthony C. Davison,et al.  Bootstrap Methods and Their Application , 1998 .

[23]  Grace L. Yang,et al.  Festschrift for Lucien Le Cam , 1997 .

[24]  Michael C. Denham,et al.  Prediction intervals in partial least squares , 1997 .

[25]  Peter L. Bonate,et al.  Approximate confidence intervals in calibration using the bootstrap , 1993 .

[26]  Hein Putter,et al.  On a Set of the First Category , 1997 .

[27]  J Carpenter,et al.  Bootstrap confidence intervals: when, which, what? A practical guide for medical statisticians. , 2000, Statistics in medicine.

[28]  P. Hall.  The Bootstrap and Edgeworth Expansion , 1992 .

[29]  J. E. Jackson.  A User's Guide to Principal Components , 1991 .

[30]  R. Lodder,et al.  Quantile BEAST Attacks the False-Sample Problem in Near-Infrared Reflectance Analysis , 1988 .

[31]  G. Meinrath.  Robust spectral analysis by moving block bootstrap designs , 2000 .