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2015 | OriginalPaper | Chapter

22. Strongly Consistent Detection for Nonparametric Hypotheses

Authors : László Györfi, Harro Walk

Published in: Measures of Complexity

Publisher: Springer International Publishing

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Abstract

Consider two robust detection problems formulated by nonparametric hypotheses such that both hypotheses are composite and indistinguishable. Strongly consistent testing rules are shown.

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Literature
2.
go back to reference Beirlant, J., Devroye, L., Györfi, L., Vajda, I.: Large deviations of divergence measures on partitions. J. Stat. Plan. Inference 93(1–2), 1–16 (2001)CrossRefMATH Beirlant, J., Devroye, L., Györfi, L., Vajda, I.: Large deviations of divergence measures on partitions. J. Stat. Plan. Inference 93(1–2), 1–16 (2001)CrossRefMATH
3.
go back to reference Biau, G., Györfi, L.: On the asymptotic properties of a nonparametric \(l_1\)-test statistic of homogeneity. IEEE Trans. Inf. Theory 51(11), 3965–3973 (2005)CrossRefMATH Biau, G., Györfi, L.: On the asymptotic properties of a nonparametric \(l_1\)-test statistic of homogeneity. IEEE Trans. Inf. Theory 51(11), 3965–3973 (2005)CrossRefMATH
4.
6.
go back to reference Devroye, L., Györfi, L.: Nonparametric Density Estimation: The \(L_1\) View. Wiley, New York (1985) Devroye, L., Györfi, L.: Nonparametric Density Estimation: The \(L_1\) View. Wiley, New York (1985)
8.
go back to reference Devroye, L., Györfi, L., Lugosi, G.: A note on robust hypothesis testing. IEEE Trans. Inf. Theory 48(7), 2111–2114 (2002)CrossRefMATH Devroye, L., Györfi, L., Lugosi, G.: A note on robust hypothesis testing. IEEE Trans. Inf. Theory 48(7), 2111–2114 (2002)CrossRefMATH
10.
go back to reference Gretton, A., Györfi, L.: Consistent nonparametric tests of independence. J. Mach. Learn. Res. 11, 1391–1423 (2010)MathSciNetMATH Gretton, A., Györfi, L.: Consistent nonparametric tests of independence. J. Mach. Learn. Res. 11, 1391–1423 (2010)MathSciNetMATH
11.
go back to reference Györfi, L., Györfi, Z., Vajda, I.: A strong law of large numbers and some applications. Stud. Sci. Math. Hung. 12, 233–244 (1977)MATH Györfi, L., Györfi, Z., Vajda, I.: A strong law of large numbers and some applications. Stud. Sci. Math. Hung. 12, 233–244 (1977)MATH
12.
go back to reference Györfi, L., Kohler, M., Krzyżak, A., Walk, H.: Distribution-Free Theory of Nonparametric Regression. Springer, New York (2002)CrossRefMATH Györfi, L., Kohler, M., Krzyżak, A., Walk, H.: Distribution-Free Theory of Nonparametric Regression. Springer, New York (2002)CrossRefMATH
13.
go back to reference Györfi, L., Masry, E.: The \(L_1\) and \(L_2\) strong consistency of recursive kernel density estimation from dependent samples. IEEE Trans. Inf. Theory 36(3), 531–539 (1990)CrossRefMATH Györfi, L., Masry, E.: The \(L_1\) and \(L_2\) strong consistency of recursive kernel density estimation from dependent samples. IEEE Trans. Inf. Theory 36(3), 531–539 (1990)CrossRefMATH
14.
go back to reference Györfi, L., van der Meulen, E.C.: A consistent goodness of fit test based on the total variation distance. In: Roussas, G. (ed.) Nonparametric Functional Estimation and Related Topics, pp. 631–645. Kluwer, Dordrecht (1990) Györfi, L., van der Meulen, E.C.: A consistent goodness of fit test based on the total variation distance. In: Roussas, G. (ed.) Nonparametric Functional Estimation and Related Topics, pp. 631–645. Kluwer, Dordrecht (1990)
15.
go back to reference Györfi, L., Walk, H.: Strongly consistent nonparametric tests of conditional independence. Stat. Probab. Lett. 82(6), 1145–1150 (2012)CrossRefMATH Györfi, L., Walk, H.: Strongly consistent nonparametric tests of conditional independence. Stat. Probab. Lett. 82(6), 1145–1150 (2012)CrossRefMATH
16.
18.
go back to reference Kraft, C.: Some conditions for consistency and uniform consistency of statistical procedures. Univ. Calif. Publ. Stat. 2, 125–142 (1955)MathSciNet Kraft, C.: Some conditions for consistency and uniform consistency of statistical procedures. Univ. Calif. Publ. Stat. 2, 125–142 (1955)MathSciNet
19.
go back to reference Le Cam, L.: Convergence of estimates under dimensionality restrictions. Ann. Stat. 1(1), 38–53 (1973)CrossRefMATH Le Cam, L.: Convergence of estimates under dimensionality restrictions. Ann. Stat. 1(1), 38–53 (1973)CrossRefMATH
20.
go back to reference Le Cam, L., Schwartz, L.: A necessary and sufficient condition for the existence of consistent estimates. Ann. Math. Stat. 31(1), 140–150 (1960)CrossRefMATH Le Cam, L., Schwartz, L.: A necessary and sufficient condition for the existence of consistent estimates. Ann. Math. Stat. 31(1), 140–150 (1960)CrossRefMATH
21.
go back to reference Robbins, H.: Statistical methods related to the law of the iterated logarithm. Ann. Math. Stat. 41(5), 1397–1409 (1970)CrossRefMATH Robbins, H.: Statistical methods related to the law of the iterated logarithm. Ann. Math. Stat. 41(5), 1397–1409 (1970)CrossRefMATH
22.
go back to reference Scheffé, H.: A useful convergence theorem for probability distributions. Ann. Math. Stat. 18(3), 434–438 (1947)CrossRefMATH Scheffé, H.: A useful convergence theorem for probability distributions. Ann. Math. Stat. 18(3), 434–438 (1947)CrossRefMATH
23.
go back to reference Schwartz, L.: On Bayes procedures. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 4(1), 10–26 (1965)CrossRefMATH Schwartz, L.: On Bayes procedures. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 4(1), 10–26 (1965)CrossRefMATH
24.
go back to reference Sen, P.K.: Sequential Nonparametrics: Invariance Principles and Statistical Inference. Wiley, New York (1981)MATH Sen, P.K.: Sequential Nonparametrics: Invariance Principles and Statistical Inference. Wiley, New York (1981)MATH
Metadata
Title
Strongly Consistent Detection for Nonparametric Hypotheses
Authors
László Györfi
Harro Walk
Copyright Year
2015
DOI
https://doi.org/10.1007/978-3-319-21852-6_22

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