Hypothesis test to compare the equality among \(k\)-populations. (Spanish. English summary) Zbl 07578264
Summary: In this paper we study a test to contrast the equality among the origen distributions of \(k\)-independent samples. The proposed statistic, denoted as \(LG_k\), is based in a measure which generalizes the \(L_1\)-norm among density functions and it allows us to compare \(k\)-different densities. From this measure and the kernel density estimation, a \(k\)-sample test for independent populations is developed. We make a wide simulation study for the proposed test and we compare its power with other nonparametric \(k\)-sample test, by considering a total of eight different statistics. We also analyze the topic of the bandwidth selection and make the same proposals about this problem.
MSC:
| 62-XX | Statistics |
References:
| [1] | Anderson, N. H., Hall, P. & Titterington, D. M. (1994), ‘Two-Sample Test Statistics for Measuring Discrepancies Between Two Multivariate Probability Density Functions using Kernel-Based Density Estimates´, Journal of Multivariate Analysis 50, 41-54. · Zbl 0798.62055 |
| [2] | Cao, R. & Van Keilegom, I. (2006), ‘Empirical Likelihood Tests for Two-Sample Problems via Nonparametric Density Estimation´, Canad. J. Statist. 34, 61-77. · Zbl 1096.62038 |
| [3] | Conover, W. J. (1965), ‘Several k-sample Kolmogorov-Smirnov tests´, Annals of Math. Statistics 36, 1019-1026. · Zbl 0173.46601 |
| [4] | Devroye, L. & Gyorfi, L. (1985), Nonparametric Density Estimation. The L_1-View, Wiley, New York, United States. · Zbl 0546.62015 |
| [5] | Hall, P., DiCiccio, J. T. & Romano, J. P. (1989), ‘On Smoothing and the Bootstrap´, Annals of Statistics 17(2), 692-704. · Zbl 0672.62051 |
| [6] | Horvath, L. (1991), ‘On L_p-Norms of Multivariate Density Estimations´, Annals of Statistics 19(4), 1933-1949. · Zbl 0765.62045 |
| [7] | Kiefer, J. (1959), ‘K-Sample Analogues of the Kolmogorov-Smirnov, Cramér-Von Mises Test´, Ann. Math. Statist. 30, 420-447. · Zbl 0134.36707 |
| [8] | Kruskal, W. H. & Wallis, W. A. (1952), ‘Use of Ranks in One-Criterion Variance Analysis´, Journal of the American Statistical Association 47(260), 583-621. · Zbl 0048.11703 |
| [9] | Lewis, J. L. (1972), ‘A k-Sample Test Based on Range Intervals´, Biometrika 59(1), 155-160. · Zbl 0245.62025 |
| [10] | Nadaraya, E. A. (1964), ‘Some new Estimates for Distribution Functions´, Theory Prob. Appl. 9, 497-500. · Zbl 0152.17605 |
| [11] | R Development Core Team, (2007), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. *http://www.R-project.org |
| [12] | Rosenblatt, M. (1956), ‘Remarks on Some nonparametric Estimates of a Density Functions´, Annals Math. Statistics 27, 832-837. · Zbl 0073.14602 |
| [13] | Scholz, F. W. & Stephens, M. A. (1987), ‘K-Samples Anderson-Darling Test´, J. Amer. Statist. Assoc. 82, 918-924. |
| [14] | Silverman, B. W. (1986), Density Estimation for Statistics and Data Analysis, Chapman & Hall, London, United Kingdom. · Zbl 0617.62042 |
| [15] | Wand, M. P. & Jones, M. C. (1995), Kernel Smoothing, Chapman & Hall, London, United Kingdom. · Zbl 0854.62043 |
| [16] | Zhang, J. & Wu, Y. (2007), ‘K-Sample Tests Based on the Likelihood Ratio´, Comput. Stat. Data Anal. 51(9), 4682-4691. · Zbl 1162.62354 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
