Robust Hypothesis Testing via Lq-Likelihood. Qin, Y. & Priebe, C., E. arXiv preprint, 10, 2013.
abstract   bibtex   
In this article, we introduce a robust testing procedure --- the Lq-likelihood ratio test (LqLR). We derive the asymptotic distribution of our test statistic and demonstrate its robustness properties both analytically and numerically. We further investigate the properties of its influence function and breakdown point. We also propose a method for selecting the tuning parameter q, and demonstrate that, with the q selected using our approach, the LqLR attains an excellent efficiency/robustness trade-off compared to the traditional likelihood ratio test (LR) and other robust tests. For the special case of testing the location parameter in the presence of gross error contamination, we show that LqLR dominates the Wilcoxon-Mann-Whitney test and the sign test at different levels of contamination.
@article{
 title = {Robust Hypothesis Testing via Lq-Likelihood},
 type = {article},
 year = {2013},
 identifiers = {[object Object]},
 pages = {30},
 websites = {http://arxiv.org/abs/1310.7278},
 month = {10},
 day = {27},
 id = {da64423f-b88b-3e3e-a354-3b29bd1d9ded},
 created = {2015-06-19T08:32:44.000Z},
 accessed = {2015-06-19},
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 profile_id = {182bbbf9-24a3-3af3-9ed6-563e8f89259b},
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 last_modified = {2015-06-19T08:32:44.000Z},
 read = {false},
 starred = {true},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Qin2013c},
 genre = {Applications},
 abstract = {In this article, we introduce a robust testing procedure --- the Lq-likelihood ratio test (LqLR). We derive the asymptotic distribution of our test statistic and demonstrate its robustness properties both analytically and numerically. We further investigate the properties of its influence function and breakdown point. We also propose a method for selecting the tuning parameter q, and demonstrate that, with the q selected using our approach, the LqLR attains an excellent efficiency/robustness trade-off compared to the traditional likelihood ratio test (LR) and other robust tests. For the special case of testing the location parameter in the presence of gross error contamination, we show that LqLR dominates the Wilcoxon-Mann-Whitney test and the sign test at different levels of contamination.},
 bibtype = {article},
 author = {Qin, Yichen and Priebe, Carey E.},
 journal = {arXiv preprint}
}

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