Averaged Stochastic Approximation for Sequential Fixed-Width Confidence Intervals under Right Censoring

Boltaeva, Nargiza

Ўзбекистон Миллий университети хабарлари · 2026-yil

Annotatsiya

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 andmust 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 andChow–Robbins efficiency (N ε /n ε → 1 a.s. and in mean). The analysis relies on an asymptoticallylinear representation of the averaged estimator, whose remainder is controlled almost surely via themartingale structure of the score. We show that stopping-time efficiency holds for every gain, whilethe 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 thestopping rule collapses the procedure.

Maqola ma’lumotlari
MualliflarBoltaeva, Nargiza
JurnalЎзбекистон Миллий университети хабарлари
NashriyotЎзбекистон Миллий университети
ISSN2181-7324, 3093-8996
Nashr sanasi2026-10-07
Jild2
Son2.3
Betlar59-67
TilIngliz
Indeksga qo‘shilgan2026-10-08

Maqolaning asl sahifasi

Kalit so‘zlar

sequential estimation, fixed-width confidence intervals, right-censoring, stochastic ap- proximation, Polyak–Ruppert averaging, Anscombe’s theorem.

Iqtibos keltirish

APABoltaeva, Nargiza (2026). Averaged Stochastic Approximation for Sequential Fixed-Width Confidence Intervals under Right Censoring. Ўзбекистон Миллий университети хабарлари, 2(2.3), 59-67. https://journals.nuu.uz/index.php/actanuuz/article/view/15247
GOST (OAK)Boltaeva, Nargiza Averaged Stochastic Approximation for Sequential Fixed-Width Confidence Intervals under Right Censoring // Ўзбекистон Миллий университети хабарлари. – 2026. – T. 2, № 2.3. – P. 59-67.
MLABoltaeva, Nargiza. “Averaged Stochastic Approximation for Sequential Fixed-Width Confidence Intervals under Right Censoring.” Ўзбекистон Миллий университети хабарлари, 2(2.3), 59-67, 2026. https://journals.nuu.uz/index.php/actanuuz/article/view/15247
ChicagoBoltaeva, Nargiza. “Averaged Stochastic Approximation for Sequential Fixed-Width Confidence Intervals under Right Censoring.” Ўзбекистон Миллий университети хабарлари, 2(2.3), 59-67 (2026). https://journals.nuu.uz/index.php/actanuuz/article/view/15247
HarvardBoltaeva, Nargiza (2026) ‘Averaged Stochastic Approximation for Sequential Fixed-Width Confidence Intervals under Right Censoring’, Ўзбекистон Миллий университети хабарлари, 2(2.3), 59-67. https://journals.nuu.uz/index.php/actanuuz/article/view/15247
BibTeX
@article{boltaevanargiza2026,
  title = {Averaged Stochastic Approximation for Sequential Fixed-Width Confidence Intervals under Right Censoring},
  author = {Boltaeva, Nargiza},
  journal = {Ўзбекистон Миллий университети хабарлари},
  year = {2026},
  volume = {2},
  number = {2.3},
  pages = {59-67},
  url = {https://journals.nuu.uz/index.php/actanuuz/article/view/15247}
}

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