Geodesic
On some testing of hypothesis problems with information constraints
Teoriâ veroâtnostej i ee primeneniâ, Tome 45 (2000) no. 4, pp. 625-638

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A problem of hypothesis testing is considered where some part of the data cannot be directly observed. Our helper observes those data and can send us some limited amount of information about them. What kind of information allows us to make the best statistical inferences? In particular, what is the minimal information sufficient in order to get the same results as if we could directly observe all the data? Some upper bounds for that minimal amount of information and some related results are obtained. A problem of hypothesis testing is considered where some part of the data cannot be directlyobserved. Our helper observes those data and can send us some limited amount of information about them. What kind of information allows us to make the best statistical inferences? In particular, what is the minimal information sufficient in order to get the same results as if we could directly observe all the data? Some upper bounds for that minimal amount of information and some related results are obtained.
Keywords: hypothesis testing, error probability, rate of transmission, critical rate. 
@article{TVP_2000_45_4_a0,
     author = {M. V. Burnashev and Shun-ichi Amari and T. S. Han},
     title = {On some testing of hypothesis problems with information constraints},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {625--638},
     publisher = {mathdoc},
     volume = {45},
     number = {4},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2000_45_4_a0/}
}
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M. V. Burnashev; Shun-ichi Amari; T. S. Han. On some testing of hypothesis problems with information constraints. Teoriâ veroâtnostej i ee primeneniâ, Tome 45 (2000) no. 4, pp. 625-638. http://geodesic.mathdoc.fr/item/TVP_2000_45_4_a0/