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Volumn 35, Issue 5, 2007, Pages 2018-2053

Goodness-of-fit tests via phi-divergences

Author keywords

Alternatives; Combining p values; Confidence bands; Goodness of fit; Hellinger; Large deviations; Multiple comparisons; Normalized empirical process; Phi divergence; Poisson boundaries

Indexed keywords


EID: 50449083797     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/0009053607000000244     Document Type: Article
Times cited : (124)

References (43)
  • 1
    • 0011576464 scopus 로고
    • Exact Bahadur efficiencies for the Kolmogorov-Smirnov and Kuiper one- and two-sample statistics
    • ABRAHAMSON, I. G. (1967). Exact Bahadur efficiencies for the Kolmogorov-Smirnov and Kuiper one- and two-sample statistics. Ann. Math. Statist. 38 1475-1490.
    • (1967) Ann. Math. Statist , vol.38 , pp. 1475-1490
    • ABRAHAMSON, I.G.1
  • 2
    • 0001199215 scopus 로고
    • A general class of coefficients of divergence of one distribution from another
    • ALI, S. M. and SILVEY, S. D. (1966). A general class of coefficients of divergence of one distribution from another. J. Roy. Statist. Soc. Ser. B 28 131-142.
    • (1966) J. Roy. Statist. Soc. Ser. B , vol.28 , pp. 131-142
    • ALI, S.M.1    SILVEY, S.D.2
  • 3
    • 0000923503 scopus 로고
    • Asymptotic theory of certain "goodness of fit" criteria based on stochastic processes
    • ANDERSON, T. W. and DARLING, D. A. (1952). Asymptotic theory of certain "goodness of fit" criteria based on stochastic processes. Ann. Math. Statist. 23 193-212.
    • (1952) Ann. Math. Statist , vol.23 , pp. 193-212
    • ANDERSON, T.W.1    DARLING, D.A.2
  • 4
    • 0041289058 scopus 로고
    • Relatively optimal combinations of test statistics
    • BERK, R. H. and JONES, D. H. (1978). Relatively optimal combinations of test statistics. Scand. J. Statist. 5 158-162.
    • (1978) Scand. J. Statist , vol.5 , pp. 158-162
    • BERK, R.H.1    JONES, D.H.2
  • 5
    • 0007329674 scopus 로고
    • Goodness-of-fit test statistics that dominate the Kolmogorov statistics
    • BERK, R. H. and JONES, D. H. (1979). Goodness-of-fit test statistics that dominate the Kolmogorov statistics. Z. Wahrsch. Verw. Gebiete 47 47-59.
    • (1979) Z. Wahrsch. Verw. Gebiete , vol.47 , pp. 47-59
    • BERK, R.H.1    JONES, D.H.2
  • 6
    • 0000797991 scopus 로고
    • On some global measures of the deviations of density function estimates
    • BICKEL, P. J. and ROSENBLATT, M. (1973). On some global measures of the deviations of density function estimates. Ann. Statist. 1 1071-1095.
    • (1973) Ann. Statist , vol.1 , pp. 1071-1095
    • BICKEL, P.J.1    ROSENBLATT, M.2
  • 7
    • 50449095031 scopus 로고    scopus 로고
    • Estimation and confidence sets for sparse normal mixtures
    • To appear
    • CAI, T. T., JIN, J. and LOW, M. G. (2005). Estimation and confidence sets for sparse normal mixtures. Ann. Statist. To appear.
    • (2005) Ann. Statist
    • CAI, T.T.1    JIN, J.2    LOW, M.G.3
  • 8
    • 25144489150 scopus 로고    scopus 로고
    • Higher criticism statistic: Detecting and identifying non-Gaussianity in the WMAP first-year data
    • CAYÓN, L., JIN, J. and TREASTER, A. (2005). Higher criticism statistic: Detecting and identifying non-Gaussianity in the WMAP first-year data. Monthly Notices Royal Astronomical Soc. 362 826-832.
    • (2005) Monthly Notices Royal Astronomical Soc , vol.362 , pp. 826-832
    • CAYÓN, L.1    JIN, J.2    TREASTER, A.3
  • 9
    • 0000182415 scopus 로고
    • A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations
    • CHERNOFF, H. (1952). A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Ann. Math. Statist. 23 493-507.
    • (1952) Ann. Math. Statist , vol.23 , pp. 493-507
    • CHERNOFF, H.1
  • 11
    • 0001856347 scopus 로고
    • Eine informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizität von Markoffschen Ketten.
    • CSISZÁR, I. (1963). Eine informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizität von Markoffschen Ketten. Magyar Tud. Akad. Mat. Kutató Int. Közl. 8 85-108.
    • (1963) Magyar Tud. Akad. Mat. Kutató Int. Közl , vol.8 , pp. 85-108
    • CSISZÁR, I.1
  • 12
    • 0000489740 scopus 로고
    • Information-type measures of difference of probability distributions and indirect observations
    • CSISZÁR, I. (1967). Information-type measures of difference of probability distributions and indirect observations. Studia Sci. Math. Hungar. 2 299-318.
    • (1967) Studia Sci. Math. Hungar , vol.2 , pp. 299-318
    • CSISZÁR, I.1
  • 13
    • 50449101814 scopus 로고    scopus 로고
    • D'AGOSTINO, R. B. and STEPHENS, M. A. (1986). Goodness-of-fit Techniques. Dekker, New York.
    • D'AGOSTINO, R. B. and STEPHENS, M. A. (1986). Goodness-of-fit Techniques. Dekker, New York.
  • 14
    • 84972504048 scopus 로고
    • A limit theorem for the maximum of normalized sums of independent random variables
    • DARLING, D. A. and ERDÖS, P. (1956). A limit theorem for the maximum of normalized sums of independent random variables. Duke Math. J. 23 143-155.
    • (1956) Duke Math. J , vol.23 , pp. 143-155
    • DARLING, D.A.1    ERDÖS, P.2
  • 15
    • 23744475601 scopus 로고    scopus 로고
    • Higher criticism for detecting sparse heterogeneous mixtures
    • DONOHO, D. and JIN, J. (2004). Higher criticism for detecting sparse heterogeneous mixtures. Ann. Statist. 32 962-994.
    • (2004) Ann. Statist , vol.32 , pp. 962-994
    • DONOHO, D.1    JIN, J.2
  • 17
    • 0001268731 scopus 로고
    • The asymptotic distribution of the suprema of the standardized empirical processes
    • EICKER, F. (1979). The asymptotic distribution of the suprema of the standardized empirical processes. Ann. Statist. 7 116-138.
    • (1979) Ann. Statist , vol.7 , pp. 116-138
    • EICKER, F.1
  • 18
    • 33344455299 scopus 로고    scopus 로고
    • Empirical likelihood based hypothesis testing
    • EINMAHL, J. H. J. and MCKEAGUE, I. W. (2003). Empirical likelihood based hypothesis testing. Bernoulli 9 267-290.
    • (2003) Bernoulli , vol.9 , pp. 267-290
    • EINMAHL, J.H.J.1    MCKEAGUE, I.W.2
  • 19
    • 0011574868 scopus 로고
    • Large deviations of goodness of fit statistics and linear combinations of order statistics
    • GROENEBOOM, P. and SHORACK, G. R. (1981). Large deviations of goodness of fit statistics and linear combinations of order statistics. Ann. Probab. 9 971-987.
    • (1981) Ann. Probab , vol.9 , pp. 971-987
    • GROENEBOOM, P.1    SHORACK, G.R.2
  • 20
    • 23744499545 scopus 로고    scopus 로고
    • Some problems of hypothesis testing leading to infinitely divisible distributions
    • INGSTER, Y. I. (1997). Some problems of hypothesis testing leading to infinitely divisible distributions. Math. Methods Statist. 6 47-69.
    • (1997) Math. Methods Statist , vol.6 , pp. 47-69
    • INGSTER, Y.I.1
  • 22
    • 0001268727 scopus 로고
    • The asymptotic distribution of the supremum of the standardized empirical distribution function on subintervals
    • JAESCHKE, D. (1979). The asymptotic distribution of the supremum of the standardized empirical distribution function on subintervals. Ann. Statist. 7 108-115.
    • (1979) Ann. Statist , vol.7 , pp. 108-115
    • JAESCHKE, D.1
  • 24
    • 50449101484 scopus 로고    scopus 로고
    • JAGER, L. and WELLNER, J. A. (2004). A new goodness of fit test: The reversed Berk-Jones statistic. Technical report, Dept. Statistics, Univ. Washington.
    • JAGER, L. and WELLNER, J. A. (2004). A new goodness of fit test: The reversed Berk-Jones statistic. Technical report, Dept. Statistics, Univ. Washington.
  • 25
    • 50449104420 scopus 로고    scopus 로고
    • On the "Poisson boundaries" of the family of weighted Kolmogorov statistics
    • A. DasGupta, ed, IMS, Beachwood, OH
    • JAGER, L. and WELLNER, J. A. (2004). On the "Poisson boundaries" of the family of weighted Kolmogorov statistics. In A Festschrift for Herman Rubin (A. DasGupta, ed.) 319-331. IMS, Beachwood, OH.
    • (2004) A Festschrift for Herman Rubin , pp. 319-331
    • JAGER, L.1    WELLNER, J.A.2
  • 27
    • 0034372869 scopus 로고    scopus 로고
    • Global power functions of goodness of fit tests
    • JANSSEN, A. (2000). Global power functions of goodness of fit tests. Ann. Statist. 28 239-253.
    • (2000) Ann. Statist , vol.28 , pp. 239-253
    • JANSSEN, A.1
  • 28
    • 50449105024 scopus 로고    scopus 로고
    • Detecting a target in very noisy data from multiple looks
    • A. DasGupta, ed, IMS, Beachwood, OH
    • JIN, J. (2004). Detecting a target in very noisy data from multiple looks. In A Festschrift for Herman Rubin (A. DasGupta, ed.) 255-286. IMS, Beachwood, OH.
    • (2004) A Festschrift for Herman Rubin , pp. 255-286
    • JIN, J.1
  • 30
    • 0032341556 scopus 로고    scopus 로고
    • Goodness of fit tests for "chimeric" alternatives
    • KHMALADZE, E. V. (1998). Goodness of fit tests for "chimeric" alternatives. Statist. Neerlandica 52 90-111.
    • (1998) Statist. Neerlandica , vol.52 , pp. 90-111
    • KHMALADZE, E.V.1
  • 31
    • 0035439009 scopus 로고    scopus 로고
    • Calculation of noncrossing probabilities for Poisson processes and its corollaries
    • KHMALADZE, E. and SHINJIKASHVILI, E. (2001). Calculation of noncrossing probabilities for Poisson processes and its corollaries. Adv. in Appl. Probab. 33 702-716.
    • (2001) Adv. in Appl. Probab , vol.33 , pp. 702-716
    • KHMALADZE, E.1    SHINJIKASHVILI, E.2
  • 33
    • 27944433393 scopus 로고    scopus 로고
    • Estimating the proportion of false null hypotheses among a large number of independently tested hypotheses
    • MEINSHAUSEN, N. and RICE, J. (2006). Estimating the proportion of false null hypotheses among a large number of independently tested hypotheses. Ann. Statist. 34 373-393.
    • (2006) Ann. Statist , vol.34 , pp. 373-393
    • MEINSHAUSEN, N.1    RICE, J.2
  • 35
    • 0003115536 scopus 로고
    • The calculation of distributions of two-sided Kolmogorov-Smirnov type statistics
    • NOÉ, M. (1972). The calculation of distributions of two-sided Kolmogorov-Smirnov type statistics. Ann. Math. Statist. 43 58-64.
    • (1972) Ann. Math. Statist , vol.43 , pp. 58-64
    • NOÉ, M.1
  • 36
    • 21844484845 scopus 로고
    • Nonparametric likelihood confidence bands for a distribution function
    • OWEN, A. B. (1995). Nonparametric likelihood confidence bands for a distribution function. J. Amer. Statist. Assoc. 90 516-521.
    • (1995) J. Amer. Statist. Assoc , vol.90 , pp. 516-521
    • OWEN, A.B.1
  • 37
    • 0009386310 scopus 로고
    • A joint study of the Kolmogorov-Smirnov and the Eicker-Jaeschke statistics
    • RÉVÉSZ, P. (1982/83). A joint study of the Kolmogorov-Smirnov and the Eicker-Jaeschke statistics. Statist. Decisions 1 57-65.
    • (1982) Statist. Decisions , vol.1 , pp. 57-65
    • RÉVÉSZ, P.1
  • 40
    • 0011399956 scopus 로고
    • Distributions related to linear bounds for the empirical distribution function
    • WELLNER, J. A. (1977). Distributions related to linear bounds for the empirical distribution function. Ann. Statist. 5 1003-1016.
    • (1977) Ann. Statist , vol.5 , pp. 1003-1016
    • WELLNER, J.A.1
  • 41
    • 0007013395 scopus 로고
    • A Glivenko-Cantelli theorem and strong laws of large numbers for functions of order statistics
    • WELLNER, J. A. (1977). A Glivenko-Cantelli theorem and strong laws of large numbers for functions of order statistics. Ann. Statist. 5 473-480.
    • (1977) Ann. Statist , vol.5 , pp. 473-480
    • WELLNER, J.A.1
  • 42
    • 0002812608 scopus 로고
    • Limit theorems for the ratio of the empirical distribution function to the true distribution function
    • WELLNER, J. A. (1978). Limit theorems for the ratio of the empirical distribution function to the true distribution function. Z. Wahrsch. Verw. Gebiete 45 73-88.
    • (1978) Z. Wahrsch. Verw. Gebiete , vol.45 , pp. 73-88
    • WELLNER, J.A.1
  • 43
    • 24344464682 scopus 로고    scopus 로고
    • A note on the asymptotic distribution of Berk-Jones type statistics under the null hypothesis
    • J. Hoffmann- Jørgensen, M. B. Marcus and J. A. Wellner, eds, Birkhäuser, Basel
    • WELLNER, J. A. and KOLTCHINSKII, V. (2003). A note on the asymptotic distribution of Berk-Jones type statistics under the null hypothesis. In High Dimensional Probability III (J. Hoffmann- Jørgensen, M. B. Marcus and J. A. Wellner, eds.) 321-332. Birkhäuser, Basel.
    • (2003) High Dimensional Probability III , pp. 321-332
    • WELLNER, J.A.1    KOLTCHINSKII, V.2


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