TY - JOUR
T1 - Large deviations application to Billingsley's example
AU - Liptser, Robert
PY - 2010
Y1 - 2010
N2 - We consider a classical model related to an empirical distribution function sequence of random variables, supported on the interval [0,1], with continuous distribution function F(t) = P(ξ1 ≤ t). Applying "Stopping Time Techniques", we give a proof of Kolmogorov's exponential bound conjectured by Kolmogorov in 1943. Using this bound we establish a best possible logarithmic asymptotic of with rate slower than 1/n for any α ε (0,1/2).
AB - We consider a classical model related to an empirical distribution function sequence of random variables, supported on the interval [0,1], with continuous distribution function F(t) = P(ξ1 ≤ t). Applying "Stopping Time Techniques", we give a proof of Kolmogorov's exponential bound conjectured by Kolmogorov in 1943. Using this bound we establish a best possible logarithmic asymptotic of with rate slower than 1/n for any α ε (0,1/2).
KW - Empirical distribution
KW - Large deviations principle
KW - Stopping time
UR - http://www.scopus.com/inward/record.url?scp=77954445141&partnerID=8YFLogxK
U2 - 10.1080/07474946.2010.487429
DO - 10.1080/07474946.2010.487429
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AN - SCOPUS:77954445141
SN - 0747-4946
VL - 29
SP - 263
EP - 274
JO - Sequential Analysis
JF - Sequential Analysis
IS - 3
ER -