TY - GEN

T1 - What you can do with coordinated samples

AU - Cohen, Edith

AU - Kaplan, Haim

PY - 2013

Y1 - 2013

N2 - Sample coordination, where similar instances have similar samples, was proposed by statisticians four decades ago as a way to maximize overlap in repeated surveys. Coordinated sampling had been since used for summarizing massive data sets. The usefulness of a sampling scheme hinges on the scope and accuracy within which queries posed over the original data can be answered from the sample. We aim here to gain a fundamental understanding of the limits and potential of coordination. Our main result is a precise characterization, in terms of simple properties of the estimated function, of queries for which estimators with desirable properties exist. We consider unbiasedness, nonnegativity, finite variance, and bounded estimates. Since generally a single estimator can not be optimal (minimize variance simultaneously) for all data, we propose variance competitiveness, which means that the expectation of the square on any data is not too far from the minimum one possible for the data. Surprisingly perhaps, we show how to construct, for any function for which an unbiased nonnegative estimator exists, a variance competitive estimator.

AB - Sample coordination, where similar instances have similar samples, was proposed by statisticians four decades ago as a way to maximize overlap in repeated surveys. Coordinated sampling had been since used for summarizing massive data sets. The usefulness of a sampling scheme hinges on the scope and accuracy within which queries posed over the original data can be answered from the sample. We aim here to gain a fundamental understanding of the limits and potential of coordination. Our main result is a precise characterization, in terms of simple properties of the estimated function, of queries for which estimators with desirable properties exist. We consider unbiasedness, nonnegativity, finite variance, and bounded estimates. Since generally a single estimator can not be optimal (minimize variance simultaneously) for all data, we propose variance competitiveness, which means that the expectation of the square on any data is not too far from the minimum one possible for the data. Surprisingly perhaps, we show how to construct, for any function for which an unbiased nonnegative estimator exists, a variance competitive estimator.

UR - http://www.scopus.com/inward/record.url?scp=84885207544&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-40328-6_32

DO - 10.1007/978-3-642-40328-6_32

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AN - SCOPUS:84885207544

SN - 9783642403279

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 452

EP - 467

BT - Approximation, Randomization, and Combinatorial Optimization

T2 - 16th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2013 and the 17th International Workshop on Randomization and Computation, RANDOM 2013

Y2 - 21 August 2013 through 23 August 2013

ER -