Likelihood Ratio Testing under Measurement Errors
Faculté de Mathématiques, Laboratoire de Probabilité, Statistique et Modélisation, Université Pierre et Marie Curie (Sorbonne Université), 4 place Jussieu, 75252 Paris CEDEX 05, France
Institute of Information Theory and Automation, The Czech Academy of Sciences, Pod Vodárenskou věží 4, 182 08 Prague 8, Czech Republic
Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic
Institute of Computer Science, The Czech Academy of Sciences, Pod Vodárenskou věží 2, 182 07 Prague 8, Czech Republic
Author to whom correspondence should be addressed.
Received: 13 November 2018 / Revised: 6 December 2018 / Accepted: 7 December 2018 / Published: 13 December 2018
We consider the likelihood ratio test of a simple null hypothesis (with density
) against a simple alternative hypothesis (with density
) in the situation that observations
are mismeasured due to the presence of measurement errors. Thus instead of
with unobservable parameter
and unobservable random variable
. When we ignore the presence of measurement errors and perform the original test, the probability of type I error becomes different from the nominal value, but the test is still the most powerful among all tests on the modified level. Further, we derive the minimax test of some families of misspecified hypotheses and alternatives. The test exploits the concept of pseudo-capacities elaborated by Huber and Strassen (1973) and Buja (1986). A numerical experiment illustrates the principles and performance of the novel test.
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MDPI and ACS Style
Broniatowski, M.; Jurečková, J.; Kalina, J. Likelihood Ratio Testing under Measurement Errors. Entropy 2018, 20, 966.
Broniatowski M, Jurečková J, Kalina J. Likelihood Ratio Testing under Measurement Errors. Entropy. 2018; 20(12):966.
Broniatowski, Michel; Jurečková, Jana; Kalina, Jan. 2018. "Likelihood Ratio Testing under Measurement Errors." Entropy 20, no. 12: 966.
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