Averaged Stochastic Approximation for Sequential Fixed-Width Confidence Intervals under Right Censoring
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We construct sequential fixed-width confidence intervals for a parameter of a right-
censored lifetime distribution observed as a stream, where the Fisher information is unknown and
must be learned online. The procedure combines the Polyak–Ruppert averaged Robbins–Monro esti-
mator with a recursively maintained information estimate, both updated in O(1) time and memory.
Under standard regularity and the gain condition cI > 1/2, we prove asymptotic consistency and
Chow–Robbins efficiency (N ε /n ε → 1 a.s. and in mean). The analysis relies on an asymptotically
linear representation of the averaged estimator, whose remainder is controlled almost surely via the
martingale structure of the score. We show that stopping-time efficiency holds for every gain, while
the gain condition governs coverage alone. Simulations on censored exponential and Weibull mod-
els confirm the theory and demonstrate that using the information in place of its reciprocal in the
stopping rule collapses the procedure.
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