Publication: Hypothesis testing for two discrete populations based on the Hellinger distance
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2010-02-01
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Elsevier Science Bv.
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Our interest is in the problem where independent samples are drawn from two different discrete populations, possibly with a common parameter. The goal is to test hypothesis about the parameters involved in these two samples. A number of tests are developed for the above purpose based on the Hellinger distance and penalized versions of it. The asymptotic distributions of the test statistics are derived. Extensive simulation results are provided, which illustrate the theory developed and the robustness of the methods.
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Basu and Basu, 1998 A. Basu, S. Basu, Penalized minimum disparity methods for multinomial models, Statistica Sinica, 8 (1998), pp. 841–860
Basu et al., 1996 A. Basu, I.R. Harris, S. Basu, Tests of hypothesis in discrete models based on the penalized Hellinger distance, Statistics & Probability Letters, 27 (1996), pp. 367–373
Basu et al., 1997, A. Basu, I.R. Harris, S. Basu, Minimum distance estimation: The approach using density based distances, in: G.S. Maddala, C.R. Rao (Eds.), Robust Inference, Handbook of Statistics, vol. 15, Elsevier Science, New York, NY (1997), pp. 21–48
Beran, 1977 , R. Beran, Minimum Hellinger distance estimates for parametric models, Annals of Statistics, 5 (1977), pp. 445–463
Bishop et al., 1975, M.M. Bishop, S.E. Fienberg, P.W. Holland, Discrete Multivariate Analysis: Theory and Practice, MIT Press, Cambridge, Mass (1975)
Harris and Basu, 1994, I.R. Harris, A. Basu, Hellinger distance as a penalized log likelihood, Communications in Statistics. Simulation and Computation, 23 (1994), pp. 1097–1113
Kullback, 1985, S. Kullback, Kullback information, S. Kotz, Johnson (Eds.), Encyclopedia of Statistical Sciences, vol. 4John Wiley & Sons, New York (1985), pp. 421–425
Kupperman, 1957, Kupperman, M., 1957. Further application to information theory to multivariate analysis and statistical inference. Ph.D. Dissertation, George Washington University
Lindsay, 1994 , B.G. Lindsay, Efficiency versus robustness: The case for minimum Hellinger distance and related methods, Annals of Statistics, 22 (1994), pp. 1081–1114
Mandal et al., 2008, Mandal, A., Basu, A., Pardo, L., 2008. Minimum Hellinger distance inference and the empty cell penalty: Asymptotic results. Technical Report No. ASD/2008/3, Indian Statistical Institute
Pardo, 2006, L. Pardo, Statistical Inference Based on Divergence Measures, Chapman & Hall/CRC (2006)
Salicrú et al., 1994, M. Salicrú, D. Morales, M.L. Menéndez, L. Pardo, On the applications of divergence type measures in testing statistical hypotheses, Journal of Multivariate Analysis, 51 (1994), pp. 372–391.
Sarkar and Basu, 1995, S. Sarkar, A. Basu, On disparity based robust tests for two discrete populations, Sankhya B, 57 (1995), pp. 353–364.
Sen and Singer, 1993, P.K. Sen, J.M. Singer, Large Sample Methods in Statistics, Chapman & Hall (1993).
Serfling, 1980, R. Serfling, Approximation Theorems of Mathematical Statistics, Wiley, New York (1980)
Simpson, 1987, D.G. Simpson, Minimum Hellinger distance estimation for analysis of count data, Journal of the American Statistical Association, 82 (1987), pp. 802–807
Simpson, 1989, D.G. Simpson, Hellinger deviance tests: Efficiency, breakdown points and examples, Journal of the American Statistical Association, 84 (1989), pp. 107–113