Power of A Class of Goodness-of-Fit Tests I

Christopher S. Withers; Saralees Nadarajah

ESAIM: Probability and Statistics (2009)

  • Volume: 13, page 283-300
  • ISSN: 1292-8100

Abstract

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Consider testing whether F = F0 for a continuous cdf on R = (-∞,∞) and for a random sample X1,..., Xn from F. We derive expansions of the associated asymptotic power based on the Cramer-von Mises, Kolmogorov-Smirnov and Kuiper statistics. We provide numerical illustrations using a double-exponential example with a shifted alternative.

How to cite

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Withers, Christopher S., and Nadarajah, Saralees. "Power of A Class of Goodness-of-Fit Tests I." ESAIM: Probability and Statistics 13 (2009): 283-300. <http://eudml.org/doc/250631>.

@article{Withers2009,
abstract = { Consider testing whether F = F0 for a continuous cdf on R = (-∞,∞) and for a random sample X1,..., Xn from F. We derive expansions of the associated asymptotic power based on the Cramer-von Mises, Kolmogorov-Smirnov and Kuiper statistics. We provide numerical illustrations using a double-exponential example with a shifted alternative. },
author = {Withers, Christopher S., Nadarajah, Saralees},
journal = {ESAIM: Probability and Statistics},
keywords = {Asymptotic power; Brownian bridge; goodness-of-fit; Pitman efficiency; asymptotic power; pitman efficiency},
language = {eng},
month = {7},
pages = {283-300},
publisher = {EDP Sciences},
title = {Power of A Class of Goodness-of-Fit Tests I},
url = {http://eudml.org/doc/250631},
volume = {13},
year = {2009},
}

TY - JOUR
AU - Withers, Christopher S.
AU - Nadarajah, Saralees
TI - Power of A Class of Goodness-of-Fit Tests I
JO - ESAIM: Probability and Statistics
DA - 2009/7//
PB - EDP Sciences
VL - 13
SP - 283
EP - 300
AB - Consider testing whether F = F0 for a continuous cdf on R = (-∞,∞) and for a random sample X1,..., Xn from F. We derive expansions of the associated asymptotic power based on the Cramer-von Mises, Kolmogorov-Smirnov and Kuiper statistics. We provide numerical illustrations using a double-exponential example with a shifted alternative.
LA - eng
KW - Asymptotic power; Brownian bridge; goodness-of-fit; Pitman efficiency; asymptotic power; pitman efficiency
UR - http://eudml.org/doc/250631
ER -

References

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  1. M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards Appl. Math. Ser.55. U.S. Government Printing Office, Washington, D.C. (1964).  Zbl0171.38503
  2. J. Andel, Local asymptotic power and efficiency of tests of Kolmogorov-Smirnov type. Ann. Math. Statist.38 (1967) 1705–1725.  Zbl0153.48001
  3. T.W. Anderson and D.A. Darling, Asymptotic theory of certain “goodness of fit” criteria based on stochastic processes. Ann. Math. Statist.23 (1952) 193–212.  Zbl0048.11301
  4. R. Courant and D. Hilbert, Methods of Mathematical Physics, volume I. Interscience Publishers, Inc., New York (1953).  Zbl0051.28802
  5. A. Erdelyi, W. Magnus, F. Oberhettinger and F.G. Tricomi, Higher Transcendental Functions, volume II. Robert E. Krieger Publishing Co., Inc., Melbourne, FL (1981).  Zbl0052.29502
  6. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, sixth edition. Academic Press, San Diego (2000).  Zbl0981.65001
  7. J. Hajek and Z. Sidak, Theory of Rank Tests. Academic Press, Inc., New York (1967).  Zbl0161.38102
  8. A. Janssen, Principal component decomposition of non-parametric tests. Probab. Theory Related Fields101 (1995) 193–209.  Zbl0814.62026
  9. A. Janssen, Global power functions of goodness of fit tests. Ann. Statist.28 (2000) 239–253.  Zbl1106.62329
  10. A. Janssen and F. Marohn, On statistical information of extreme order statistics, local extreme value alternatives, and Poisson point processes. J. Multiv. Anal.48 (1994) 1–30.  Zbl0801.62007
  11. C. Jordan, Calculus of Finite Differences, third edition. Chelsea Publishing Co., New York (1965).  
  12. A.N. Kolmogorov, Confidence limits for an unknown distribution function. Ann. Math. Statist.12 (1941) 461–463.  Zbl0060.30514
  13. E.L. Lehmann and J.P. Romano, Testing Statistical Hypotheses, third edition. Springer, New York (2005).  Zbl1076.62018
  14. H. Milbrodt and H. Strasser, On the asymptotic power of the two-sides Kolmogorov-Smirnov. J. Statist. Plann. Inference26 (1990) 1–23.  Zbl0728.62049
  15. E.S. Pearson and H.O. Hartley, Biometrika Tables for Statisticians, volume II. Cambridge University Press, New York (1972).  Zbl0255.62003
  16. D. Quade, On the asymptotic power of the one-sample Kolmogorov-Smirnov Tests. Ann. Math. Statist.36 (1965) 1000–1018.  Zbl0137.36903
  17. J. Rahnenführer, On preferences of general two-sided tests with applications to Kolmogorov Smirnov-type tests. Statist. Decisions21 (2003) 149–170.  Zbl1040.62033
  18. S. Shapiro and M. Wilk, An analysis of variance test for normality. Biometrika52 (1965) 591–611.  Zbl0134.36501
  19. G.R. Shorak and J.A. Wellner, Empirical Processes with Applications to Statistics. Wiley, New York (1986).  
  20. G.P. Steck, Rectangle probabilities for uniform order statistics. Ann. Math. Statist.42 (1971) 1–11.  Zbl0221.62013
  21. M.A. Stephens, The goodness-of-fit statistic VN: Distribution and significance points. Biometrika52 (1965) 309–321.  Zbl0192.26106
  22. M.A. Stephens, Tests for normality. Technical Report No. 152, November 10, 1969, Department of Statistics, Stanford University (1969).  Zbl0181.45802
  23. M.A. Stephens, Kolmogorov type tests for exponentiality. Technical Report No. 154, Department of Statistics, Stanford University (1970).  
  24. H. Strasser, Global extrapolations of local efficiency. Statist. Decisions8 (1990) 11–26.  Zbl0749.62032

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