Testing strict monotonicity in nonparametric regression

被引：13
作者：
Birke M. [1 ]
Dette H. [1 ]
机构：
[1] Ruhr-Universität Bochum, Fakultät für Mathematik
来源：
Mathematical Methods of Statistics | 2007年 / 16卷 / 2期
基金：
美国国家卫生研究院;
关键词：
goodness-of-fit test; nonparametric regression; strictly monotone regression;
D O I：
10.3103/S1066530707020032
中图分类号：
学科分类号：
摘要：
A new test for strict monotonicity of the regression function is proposed which is based on a composition of an estimate of the inverse of the regression function with a common regression estimate. This composition is equal to the identity if and only if the "true" regression function is strictly monotone, and a test based on an L 2-distance is investigated. The asymptotic normality of the corresponding test statistic is established under the null hypothesis of strict monotonicity. © 2007 Allerton Press, Inc.
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收藏
页码：110 / 123
页数：13
相关论文
共 22 条
  • [1] Baraud Y., Huet S., Laurent B., Adaptive tests of qualitative hypotheses, ESAIM, Probab. Statist., 7, pp. 147-159, (2003)
  • [2] Bowman A.W., Jones M.C., Gijbels I., Testing monotonicity of regression, J. Computational and Graphical Statist., 7, pp. 489-500, (1998)
  • [3] Brunk H.D., Maximum likelihood estimates of monotone parameters, Ann. Math. Statist., 26, pp. 607-616, (1955)
  • [4] Dette H., Neumeyer N., Pilz K.F., A simple nonparametric estimator of a monotone regression function, Bernoulli, 12, pp. 469-490, (2006)
  • [5] Dominguez-Menchero J., Gonzalez-Rodriguez G., Lopez-Palomo M.J., An L <sub>2</sub> point of view in testing monotone regression, J. Nonparam. Statist., 17, pp. 135-153, (2006)
  • [6] Durot C., A Kolmogorov-type test for monotonicity of regression, Statist. Probab. Lett., 63, pp. 425-433, (2003)
  • [7] Fan J., Gijbels I., Local Polynomial Modelling and Its Applications, (1997)
  • [8] Friedman J., Tibshirani R., The monotone smoothing of scatterplots, Technometrics, 26, pp. 243-250, (1984)
  • [9] Ghosal S., Sen A., van der Vaart A.W., Testing monotonicity of regression, Ann. Statist., 28, pp. 1054-1082, (2000)
  • [10] Gijbels I., Hall P., Jones M.C., Koch I., Tests for monotonicity of a regression mean with guaranteed level, Biometrika, 87, pp. 663-673, (2000)
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