Sequential Lq-likelihood-ratio-type test. (Chinese. English summary) Zbl 07803013
Summary: In the paper, the authors investigate the sequential Lq-likelihood-ratio-type test(for short SLqRT), and some properties of the SLqRT. Based on one of these properties-the basic identity, the power function and the average sample size of the SLqRT are obtained. In order to save cost, they select the appropriate \(q\) value for the hypothesis test of the exponential distribution by minimizing the average sample size. In addition, they also give the theoretical derivation and two simulation examples to show the robustness of the SLqRT. Moreover, they calculate the average sample sizes of sequential probability ratio test(for short SPRT) and SLqRT under the gross error model with different contamination parameters. And the results shows that the SLqRT is better than the SPRT under the average sample size.
MSC:
| 62L10 | Sequential statistical analysis |
| 62F03 | Parametric hypothesis testing |
| 62F35 | Robustness and adaptive procedures (parametric inference) |
Keywords:
sequential Lq-likelihood-ratio-type test; basic identity; power function; the optimal \(q\) value; robustnessReferences:
| [1] | Refernce(1): |
| [2] | Kim I, Park S. Likelihood ratio tests for multivariate normality [J]. Communications in Statistics-Theory and Methods, 2017, 47(8):1923-1934. [2] Krishnamoorthy K, Lee M, Wang X. Likelihood ratio tests for comparing several gamma distributions [J]. Environmetrics, 2015, 26(8):571-583. [3] Xie J S, Xiao N N. The likelihood ratio test for high-dimensional linear regression model [J]. Communications in Statistics-Theory and Methods, 2017, 46(17):8479-8492. [4] Qin Y, Priebe E C. Robust hypothesis testing via Lq-likelihood [J]. Statistica Sinica,2017, 27:1793-1813. [5] Huang C, Lin J G, Ren Y Y. Testing for the shape parameter of generalized extreme value distribution based on the Lq-likelihood ratio statistic [J]. Metrika, 2012,76(5):641-671. [6] Lai T L, Zhang L M. Nearly optimal generalized sequential likelihood ratio tests in multivariate exponential families [J]. Institute of Mathematical Statistics, 1994, 24:331-346. [7] Klein I, Matsuoka M T, Guzatto M P, et al. An approach to identify multiple outliers based on sequential likelihood ratio test [J]. Survey Review, 2017, 49(357):449-457. [8] Bangdiwala S I. A sequential likelihood ratio test for general hypotheses [J]. Sequential Analysis, 1982, 1(1):57-80. [9] Julien R, Lutz L, Francois H. Sequential likelihood ratio test for cognitive radios [J].IEEE Transactions on Signal Processing: A publication of the IEEE Signal Processing,Society, 2016, 64(24):6627-6639. [10] Lai T L, Zhang L M. A modification of Schwarz’s sequential likelihood ratio tests in multivariate sequential analysi [J]. Sequential Analysis, 1994, 13(2):79-96. [11] Ferrari D, Yang Y. Maximum Lq-likelihood estimation [J]. The Annals of Statistics,2010, 38:753-783. [12] Siegmund D. Sequential analysis: tests and confidence interval [M]. New York:Springer-Verlag, 1985. [13] Chen J D. Sequential analysis [M]. Beijing: Beijing Pulishing House, 1995. [14] Anscombe F J. Large-Sample theory of sequential estimation [J]. Mathematical Proceedings of the Cambridge Philosophical Society, 1952, 48(4):600-607. [15] Huber P J. A robust version of the probability ratio test [J]. The Annals of Mathematical Statistics, 1965, 36(6):1753-1758. [16] Jiang Y Y, Xu X Z. Likelihood ratio test for the parameters of exponentially modified Gaussian distribution [J]. Communication in Statistics-Simulation and Computation,2022:1-8. [17] Dunn R, Ramdas A, Balakrishnan S, et al. Gaussian universal likelihood ratio testing,Biometrika [J]. 2023. DOI: 10.48550/arXiv.2104.14676. [18] Gimenez P, Guarracino L, Galea M. Maximum Lq-likelihood estimation in function measurement error models [J]. Statistica Sinica, 2022, 32:1723-1743. [19] Li Y L, Hu H C. Sequential Lq -likehood ratio type test and its applications [J]. Journal of Hubei University (Natural Science), 2022, 42(04):1-5+27. |
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