Bootstrap: theory and applications

This is a review of bootstrap methods, concentrating on basic ideas and applications. It begins with an exposition of the bootstrap principle and gives several examples of its use. Bootstrap methods for testing statistical hypotheses are then reviewed and an analysis of accuracy of bootstrap tests is provided. We discuss how the bootstrap can be used to estimate variance stabilizing transformations that are crucial for the level of accuracy of bootstrap tests. Finally, we describe an application of multiple bootstrap tests to the problem of finding optimum locations of vibration sensors for knock detection in spark ignition engines.

[1]  T. W. Anderson.  An Introduction to Multivariate Statistical Analysis , 1959 .

[2]  T. W. Anderson.  An Introduction to Multivariate Statistical Analysis, 2nd Edition. , 1985 .

[3]  D. Brillinger.  The finite fourier transform of a stationary process , 1983 .

[4]  B. Efron,et al.  A Leisurely Look at the Bootstrap, the Jackknife, and , 1983 .

[5]  B. Efron.  Nonparametric standard errors and confidence intervals , 1981 .

[6]  R. Fisher.  014: On the "Probable Error" of a Coefficient of Correlation Deduced from a Small Sample. , 1921 .

[7]  Nicholas I. Fisher,et al.  Bootstrap Confidence Regions for Directional Data , 1989 .

[8]  P. Hall.  Theoretical Comparison of Bootstrap Confidence Intervals , 1988 .

[9]  R. Beran.  Prepivoting to reduce level error of confidence sets , 1987 .

[10]  B. Efron.  Better Bootstrap Confidence Intervals , 1987 .

[11]  Heinz Decker,et al.  Knock Control of Gasoline Engines-A Comparison of Solutions and Tendencies, with Special Reference to Future European Emission Legislation , 1985 .

[12]  B. Efron.  Computers and the Theory of Statistics: Thinking the Unthinkable , 1979 .

[13]  N. R. Goodman,et al.  GAUSSIAN APPROXIMATIONS TO THE DISTRIBUTION OF SAMPLE COHERENCE , 1965 .

[14]  Robert Tibshirani,et al.  Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy , 1986 .

[15]  N. R. Goodman.  Statistical analysis based on a certain multivariate complex Gaussian distribution , 1963 .