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A Two-sample Nonparametric Likelihood Ratio Test

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A Two-sample Nonparametric Likelihood Ratio Test. / Marsh, Patrick.

In: Journal of Nonparametric Statistics, Vol. 22, No. 8, 2011, p. 1053-1065.

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Marsh, P 2011, 'A Two-sample Nonparametric Likelihood Ratio Test', Journal of Nonparametric Statistics, vol. 22, no. 8, pp. 1053-1065. https://doi.org/10.1080/10485250903486078

APA

Marsh, P. (2011). A Two-sample Nonparametric Likelihood Ratio Test. Journal of Nonparametric Statistics, 22(8), 1053-1065. https://doi.org/10.1080/10485250903486078

Vancouver

Marsh P. A Two-sample Nonparametric Likelihood Ratio Test. Journal of Nonparametric Statistics. 2011;22(8):1053-1065. https://doi.org/10.1080/10485250903486078

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Marsh, Patrick. / A Two-sample Nonparametric Likelihood Ratio Test. In: Journal of Nonparametric Statistics. 2011 ; Vol. 22, No. 8. pp. 1053-1065.

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@article{afaf6319f0b14963846ae55ae3902aa6,
title = "A Two-sample Nonparametric Likelihood Ratio Test",
abstract = "This paper proposes a new test for the hypothesis that two samples have the same distribution. The likelihood ratio test of Portnoy [Portnoy, S. (1988), 'Asymptotic Behaviour of Likelihood Methods for Exponential Families When the Number of Parameters Tends to Infinity', Annals of Statistics, 16, 356-366] is applied in the context of the consistent series density estimator of Crain [Crain, B.R. (1974), 'Estimation of Distributions Using Orthogonal Expansions', Annals of Statistics, 2, 454-463] and Barron and Sheu [Barron, A.R., and Sheu, C.-H. (1991), 'Approximation of Density Functions by Sequences of Exponential Families'. Annals of Statistics, 19, 1347-1369]. It is proven that the test, when suitably standardised, is asymptotically standard normal and consistent against any complementary fixed alternative. In comparison with established tests, such as the Kolmogorov-Smirnov, Cramer-von Mises and rank sum, median, and dispersion tests, the proposed tests enjoy broadly comparable finite sample size properties, but vastly superior power properties when considered over a range of different alternatives.",
keywords = "two sample tests, series density estimator, non-parametric likelihood ratio, GOODNESS-OF-FIT, KOLMOGOROV-SMIRNOV, EXPONENTIAL-FAMILIES, CRITERION, SAMPLE",
author = "Patrick Marsh",
note = "M1 - 8",
year = "2011",
doi = "10.1080/10485250903486078",
language = "English",
volume = "22",
pages = "1053--1065",
journal = "Journal of Nonparametric Statistics",
issn = "1048-5252",
publisher = "Taylor and Francis Ltd.",
number = "8",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - A Two-sample Nonparametric Likelihood Ratio Test

AU - Marsh, Patrick

N1 - M1 - 8

PY - 2011

Y1 - 2011

N2 - This paper proposes a new test for the hypothesis that two samples have the same distribution. The likelihood ratio test of Portnoy [Portnoy, S. (1988), 'Asymptotic Behaviour of Likelihood Methods for Exponential Families When the Number of Parameters Tends to Infinity', Annals of Statistics, 16, 356-366] is applied in the context of the consistent series density estimator of Crain [Crain, B.R. (1974), 'Estimation of Distributions Using Orthogonal Expansions', Annals of Statistics, 2, 454-463] and Barron and Sheu [Barron, A.R., and Sheu, C.-H. (1991), 'Approximation of Density Functions by Sequences of Exponential Families'. Annals of Statistics, 19, 1347-1369]. It is proven that the test, when suitably standardised, is asymptotically standard normal and consistent against any complementary fixed alternative. In comparison with established tests, such as the Kolmogorov-Smirnov, Cramer-von Mises and rank sum, median, and dispersion tests, the proposed tests enjoy broadly comparable finite sample size properties, but vastly superior power properties when considered over a range of different alternatives.

AB - This paper proposes a new test for the hypothesis that two samples have the same distribution. The likelihood ratio test of Portnoy [Portnoy, S. (1988), 'Asymptotic Behaviour of Likelihood Methods for Exponential Families When the Number of Parameters Tends to Infinity', Annals of Statistics, 16, 356-366] is applied in the context of the consistent series density estimator of Crain [Crain, B.R. (1974), 'Estimation of Distributions Using Orthogonal Expansions', Annals of Statistics, 2, 454-463] and Barron and Sheu [Barron, A.R., and Sheu, C.-H. (1991), 'Approximation of Density Functions by Sequences of Exponential Families'. Annals of Statistics, 19, 1347-1369]. It is proven that the test, when suitably standardised, is asymptotically standard normal and consistent against any complementary fixed alternative. In comparison with established tests, such as the Kolmogorov-Smirnov, Cramer-von Mises and rank sum, median, and dispersion tests, the proposed tests enjoy broadly comparable finite sample size properties, but vastly superior power properties when considered over a range of different alternatives.

KW - two sample tests

KW - series density estimator

KW - non-parametric likelihood ratio

KW - GOODNESS-OF-FIT

KW - KOLMOGOROV-SMIRNOV

KW - EXPONENTIAL-FAMILIES

KW - CRITERION

KW - SAMPLE

UR - http://www.scopus.com/inward/record.url?scp=78149403550&partnerID=8YFLogxK

U2 - 10.1080/10485250903486078

DO - 10.1080/10485250903486078

M3 - Article

VL - 22

SP - 1053

EP - 1065

JO - Journal of Nonparametric Statistics

JF - Journal of Nonparametric Statistics

SN - 1048-5252

IS - 8

ER -