Robust hypothesis testing for bounded classes of probability densities
Abstract
The contributions of Huber (1964, 1965) to the theory of robust statistical inference are considered. It is shown that Huber's result for the epsiloncontamination classes can be extended to classes of probability density functions defined as bands lying between upper and lower bounds. Attention is given to least favorable densities, and aspects of distance measures and robustness. The least favorable pair of probability density functions is obtained explicitly for the binary hypothesis testing problem where allowable density functions are constrained to lie within given upper and lower bounds. The likelihoodratio tests for the least favorable pair of densities are robust in terms of performance criteria based on the risk function.
 Publication:

IEEE Transactions on Information Theory
 Pub Date:
 March 1981
 Bibcode:
 1981ITIT...27..242K
 Keywords:

 Inference;
 Probability Density Functions;
 Robustness (Mathematics);
 Signal Detection;
 Signal Processing;
 Statistical Decision Theory;
 Channel Noise;
 Hypotheses;
 Information Theory;
 Maximum Likelihood Estimates;
 Risk;
 Transmission Efficiency;
 Communications and Radar