Power of a class of goodness-of-fit tests I
ESAIM: Probability and Statistics, Tome 13 (2009), pp. 283-300.

Consider testing whether F=F 0 for a continuous cdf on R=(-,) and for a random sample X 1 ,..., X n 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.

DOI : 10.1051/ps:2008013
Classification : 62F03, 62F05, 62F12
Mots clés : asymptotic power, brownian bridge, goodness-of-fit, Pitman efficiency
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     title = {Power of a class of goodness-of-fit tests {I}},
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Withers, Christopher S.; Nadarajah, Saralees. Power of a class of goodness-of-fit tests I. ESAIM: Probability and Statistics, Tome 13 (2009), pp. 283-300. doi : 10.1051/ps:2008013. http://archive.numdam.org/articles/10.1051/ps:2008013/

[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). | MR | Zbl

[2] J. Andel, Local asymptotic power and efficiency of tests of Kolmogorov-Smirnov type. Ann. Math. Statist. 38 (1967) 1705-1725. | MR | Zbl

[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. | MR | Zbl

[4] R. Courant and D. Hilbert, Methods of Mathematical Physics, volume I. Interscience Publishers, Inc., New York (1953). | MR | Zbl

[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). | MR | Zbl

[6] I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, sixth edition. Academic Press, San Diego (2000). | MR | Zbl

[7] J. Hajek and Z. Sidak, Theory of Rank Tests. Academic Press, Inc., New York (1967). | MR | Zbl

[8] A. Janssen, Principal component decomposition of non-parametric tests. Probab. Theory Related Fields 101 (1995) 193-209. | MR | Zbl

[9] A. Janssen, Global power functions of goodness of fit tests. Ann. Statist. 28 (2000) 239-253. | MR | Zbl

[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. | MR | Zbl

[11] C. Jordan, Calculus of Finite Differences, third edition. Chelsea Publishing Co., New York (1965). | MR | Zbl

[12] A.N. Kolmogorov, Confidence limits for an unknown distribution function. Ann. Math. Statist. 12 (1941) 461-463. | MR | Zbl

[13] E.L. Lehmann and J.P. Romano, Testing Statistical Hypotheses, third edition. Springer, New York (2005). | MR | Zbl

[14] H. Milbrodt and H. Strasser, On the asymptotic power of the two-sides Kolmogorov-Smirnov. J. Statist. Plann. Inference 26 (1990) 1-23. | MR | Zbl

[15] E.S. Pearson and H.O. Hartley, Biometrika Tables for Statisticians, volume II. Cambridge University Press, New York (1972). | MR | Zbl

[16] D. Quade, On the asymptotic power of the one-sample Kolmogorov-Smirnov Tests. Ann. Math. Statist. 36 (1965) 1000-1018. | MR | Zbl

[17] J. Rahnenführer, On preferences of general two-sided tests with applications to Kolmogorov Smirnov-type tests. Statist. Decisions 21 (2003) 149-170. | MR | Zbl

[18] S. Shapiro and M. Wilk, An analysis of variance test for normality. Biometrika 52 (1965) 591-611. | MR | Zbl

[19] G.R. Shorak and J.A. Wellner, Empirical Processes with Applications to Statistics. Wiley, New York (1986). | MR | Zbl

[20] G.P. Steck, Rectangle probabilities for uniform order statistics. Ann. Math. Statist. 42 (1971) 1-11. | MR | Zbl

[21] M.A. Stephens, The goodness-of-fit statistic V N : Distribution and significance points. Biometrika 52 (1965) 309-321. | MR | Zbl

[22] M.A. Stephens, Tests for normality. Technical Report No. 152, November 10, 1969, Department of Statistics, Stanford University (1969).

[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. Decisions 8 (1990) 11-26. | MR | Zbl

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