TY - GEN

T1 - Exact Optimal Fixed Width Confidence Interval Estimation for the Mean

AU - Deep, Vikas

AU - Bassamboo, Achal

AU - Juneja, Sandeep

AU - Zeevi, Assaf

N1 - Publisher Copyright:
© 2022 IEEE.

PY - 2022

Y1 - 2022

N2 - We consider a classical problem in simulation/statistics - given i.i.d. samples of a rv, the goal is to arrive at a confidence interval (CI) of a pre-specified width varepsilon, and with a coverage guarantee that the mean lies in the CI with probability at least 1-delta for pre-specified deltain(0,1). This problem has been well studied in an asymptotic regime as varepsilon shrinks to zero. The novelty of our analysis is the derivation of the lower bound on the number of samples required by any algorithm to construct a CI of varepsilon -width with the coverage guarantee for fixed varepsilon > 0 and delta, and construction of an algorithm that, under mild assumptions, matches the lower bound. For simplicity, we present our results for rv belonging to a single parameter exponential family, and illustrate its efficacy through a numerical study.

AB - We consider a classical problem in simulation/statistics - given i.i.d. samples of a rv, the goal is to arrive at a confidence interval (CI) of a pre-specified width varepsilon, and with a coverage guarantee that the mean lies in the CI with probability at least 1-delta for pre-specified deltain(0,1). This problem has been well studied in an asymptotic regime as varepsilon shrinks to zero. The novelty of our analysis is the derivation of the lower bound on the number of samples required by any algorithm to construct a CI of varepsilon -width with the coverage guarantee for fixed varepsilon > 0 and delta, and construction of an algorithm that, under mild assumptions, matches the lower bound. For simplicity, we present our results for rv belonging to a single parameter exponential family, and illustrate its efficacy through a numerical study.

UR - http://www.scopus.com/inward/record.url?scp=85147455760&partnerID=8YFLogxK

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U2 - 10.1109/WSC57314.2022.10015355

DO - 10.1109/WSC57314.2022.10015355

M3 - Conference contribution

AN - SCOPUS:85147455760

T3 - Proceedings - Winter Simulation Conference

SP - 713

EP - 723

BT - Proceedings of the 2022 Winter Simulation Conference, WSC 2022

A2 - Feng, B.

A2 - Pedrielli, G.

A2 - Peng, Y.

A2 - Shashaani, S.

A2 - Song, E.

A2 - Corlu, C.G.

A2 - Lee, L.H.

A2 - Chew, E.P.

A2 - Roeder, T.

A2 - Lendermann, P.

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2022 Winter Simulation Conference, WSC 2022

Y2 - 11 December 2022 through 14 December 2022

ER -