Hypothesis Testing Using an L1-Distance Bootstrap

American Statistician

Volumn 51, Issue 2, 1997, Pages 145-150

  Allen, David L ^a  

^a EASTERN OREGON UNIVERSITY   (United States)

Author keywords

Bootstrap; Density estimation; Hypothesis testing; L1 distance; Nonparametric methods; Two sample problem

Indexed keywords

EID: 0031475761     PISSN: 00031305     EISSN: 15372731     Source Type: Journal    
DOI: 10.1080/00031305.1997.10473949     Document Type: Article

References (18)

1. Anderson, N., Hall, P., and Titterington, D. (1994), “Two-Sample Test Statistics for Measuring Discrepancies Between Two Multivariate Probability Density Functions Using Kernel-Based Density Estimates,” Journal of Multivariate Analysis, 50, 41—54.
2. Bowman, A. W. (1985), “A Comparative Study of Some Kernel-Based Nonparametric Density Estimators,” Journal of Statistical Computation and Simulation, 21, 313-327.
3. Bowman, A. W. (1992), “Density Based Tests for Goodness-of-Fit Journal of Statistical Computation and Simulation, 40, 1-13.
4. Bowman, A. W., and Foster, P. J. (1993), “Adaptive Smoothing and Density Based Tests of Multivariate Normality,” Journal of the American Statistical Association, 88, 529-537.
5. p Distances of Kernel Estimators of Densities Under Random Censorship,” The Annals of Statistics, 19, 1813-1831.
6. Darling, D. A. (1957), “The Kolmogorov-Smirnov, Cramer-Von Mises Tests,” The Annals of Mathematical Statistics, 28, 823-838.
7. Devroye, L., and Gyorfi, L. (1985), Nonparametric Density Estimation the L\ View, New York: Wiley.
8. Efron, B., and Tibshirani, R. (1993), An Introduction to the Bootstrap, New York: Chapman and Hall.
9. Hall, P., and Wand, M. P. (1988), “Minimizing the L\ Distance in Nonparametric Density Estimation,” Journal of Multivariate Analysis, 26, 59-88.
10. Kaigh, W. D. (1994), “Distribution-Free Two-Sample Tests Based on Rank Spacings,” Journal of the American Statistical Association, 89, 159-167.
11. Lehmann, E. L. (1959), Testing Statistical Hypotheses, New York: Wiley.
12. Mason, D. M., and Schuenemeyer, J. H. (1983), “A Modified Kolmogorov-Smirnov Test Sensitive to Tail Alternatives,” The Annals of Statistics, 11, 933-946.
13. Massey, F. J. (1951), “The Distribution of the Maximum Deviation Between Two Sample Cumulative Step Functions,” The Annals of Mathematical Statistics, 22, 125-128.
14. Nadaraya, E. A. (1989), Nonparametric Estimation of Probability Densities and Regression Curves, Boston: Kluwer Academic.
15. Noreen, E. W. (1989), Computer-Intensive Methods for Testing Hypotheses: An Introduction, New York: Wiley.
16. Parzen, E. (1962), “On Estimation of a Probability Density Function and Mode,” The Annals of Mathematical Statistics, 33, 1065-1076.
17. Rosenblatt, M. (1956), “Remarks on Some Nonparametric Estimates of a Density Function,” The Annals Mathematical Statistics, 27, 832-837.
18. Silverman, B. W. (1986), Density Estimation for Statistics and Data Analysis, London: Chapman and Hall.