A Finite Memory Test of the Irrationality of the Parameter of a Coin
Hirschler, Patrick ; Cover, Thomas M.
Ann. Statist., Tome 3 (1975) no. 1, p. 939-946 / Harvested from Project Euclid
Let $X_1,X_2,...$ be a Bernoulli sequence with parameter p. An algorithm $T_{n=1}=\\f(T_n,X_n,n)$; $d_n = d(T_n); \\f:\{1,2,\1dots,8\} \times \{0,1\} \times \{0,1, \1dots}\rightarrow \{1, \1dots, 8\}; d:\{1,2,\dots,8\} \rigtharrow \{H_0,H_1\}$; is found such that $d(T_n)= H_0$ all but a finite number of times with probability one if p is rational, and $d(T_n)= H_1$ all but a finite number of times with probability one if p is irrational (and not in a given null set of irrationals). Thus, an 8-state memory with a time-varying algorithm makes only a finite number of mistakes with probability one on determining the rationality of the parameter of a coin. Thus, determining the rationality of the Bernoulli parameter p does not depend on infinite memory of the data.
Publié le : 1975-07-14
Classification:  Finite memory,  coin,  hypothesis testing,  rationals,  62C99
@article{1176343194,
     author = {Hirschler, Patrick and Cover, Thomas M.},
     title = {A Finite Memory Test of the Irrationality of the Parameter of a Coin},
     journal = {Ann. Statist.},
     volume = {3},
     number = {1},
     year = {1975},
     pages = { 939-946},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176343194}
}
Hirschler, Patrick; Cover, Thomas M. A Finite Memory Test of the Irrationality of the Parameter of a Coin. Ann. Statist., Tome 3 (1975) no. 1, pp.  939-946. http://gdmltest.u-ga.fr/item/1176343194/