RT Journal Article
T1 Wald type and phi-divergence based test-statistics for isotonic binomial proportions.
A1 Martin, N.
A1 Mata, R.
A1 Pardo Llorente, Leandro
AB In this paper new test statistics are introduced and studied for the important problem of testing hypothesis that involves inequality constraint on proportions when the sample comes from independent binomial random variables: Wald type and phi-divergence based test-statistics. As a particular case of phi-divergence based test-statistics, the classical likelihood ratio test is considered. An illustrative example is given and the performance of all of them for small and moderate sample sizes is analyzed in an extensive simulation study. (C) 2015 International Association for Mathematics and Computers in Simulation
PB Elsevier
SN 0378-4754
YR 2016
FD 2016
LK https://hdl.handle.net/20.500.14352/24279
UL https://hdl.handle.net/20.500.14352/24279
LA eng
NO [1] R.E. Barlow, D. Bartholomew, J.M. Bremner, H.D. Brunk, Statistical Inference under Order Restrictions: The Theory and Application of Isotonic Regression, Wiley, New York,1972.[2] D.J. Bartholomew, A test of homogeneity for ordered alternatives, Biometrika 46 (1959) 36–48.[3] M.W. Browne, Asymptotically distribution-free methods for the analysis of covariance structures, Br. J. Math. Stat. Psychol. 37 (1984) 62–83.[4] R. Colombi, A. Forcina, Marginal regression models for the analysis of positive association of ordinal response variables, Biometrika 88 (2001) 1007–1019.[5] J.R. Dale, Asymptotic normality of goodness-of-fit statistics for sparse product multinomials, J. R. Stat. Soc. Series B Stat. Methodol. 48 (1986) 48–59.[6] V. Dardanoni, A. Forcina, A unified approach to likelihood inference on stochastic orderings in a nonparametric context, J. Amer. Statist.Assoc. 93 (1998) 1112–1122.[7] J.L. Fleiss, B. Levin, M.C. Paik, Statistical Methods for Rates and Proportions, third ed., Wiley, New York, 2003.[8] B.I. Graubard, E.L. Korn, Choice of column scores for testing independence in ordered 2 × I contingency tables, Biometrics 43 (1987)471–476.[9] A. Kudo, A multivariate analogue of the one-sided test, Biometrika 50 (1963) 403–418. [10] J.Y. Mancuso, H. Ahan, J.J. Chen, Order-restricted dose-related trend tests, Stat. Med. 20 (2001) 2305–2318.[11] N. Martin, N. Balakrishnan, Hypothesis testing in a generic nesting framework for general distributions, J. Multivariate Anal. 118 (2013) 1–23.[12] N. Martin, R. Mata, L. Pardo, Phi-divergence statistics for the likelihood ratio order: an approach based on log-linear models, J. Multivariate Anal. 130 (2014) 387–408.[13] M.L. Menendez, D. Morales, L. Pardo, Tests based on divergences for and against ordered alternatives in cubic contingency tables, Appl. Math. Comput. 134 (2003) 207–213.[14] L. Pardo, Statistical Inference Based on Divergence Measures, Chapman & Hall/CRC, Boca Raton, 2006.[15] T.R.C. Read, N.A.C. Cressie, Goodness of Fit Statistics for Discrete Multivariate Data, Springer-Verlag, New York,1989.[16] T. Robertson, F.T. Wright, R. Dykstra, Order Restricted Statistical Inference, John Wiley and Sons, New York, 1988.[17] P.K. Sen, M.J. Silvapulle, An appraisal of some aspects of statistical inference under inequality constraints, J. Statist. Plann. Inference 107 (2002) 3–43.[18] A. Shapiro, Asymptotic distribution of test statistics in the analysis of moment structures underinequality constraints, Biometrika 72 (1985)133–144.[19] A. Shapiro, Towards a unified theory of inequality constrained testing in multivariate analysis, Int. Stat. Rev. 56 (1988) 49–62.[20] M.J. Silvapulle, P.K. Sen, Constrained Statistical Inference: Inequality, Order, and Shape Restrictions, Wiley, New York, 2005
NO Spanish Grant
DS Docta Complutense
RD 2 may 2024