Using auxiliary information in statistical function estimation
Sergey Tarima,Dmitri Pavlov +1 more
TL;DR: In this article, a method of using auxiliary information for improving properties of the estimators based on a current sample only is proposed, assuming that the information is available as a number of estimates based on samples obtained from some other mutually independent data sources.
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Abstract: In many practical situations sample sizes are not sufficiently large and estimators based on such samples may not be satisfactory in terms of their variances. At the same time it is not unusual that some auxiliary information about the parameters of interest is available. This paper considers a method of using auxiliary information for improving properties of the estimators based on a current sample only. In particular, it is assumed that the information is available as a number of estimates based on samples obtained from some other mutually independent data sources. This method uses the fact that there is a correlation effect between estimators based on the current sample and auxiliary information from other sources. If variance covariance matrices of vectors of estimators used in the estimating procedure are known, this method produces more efficient estimates in terms of their variances compared to the estimates based on the current sample only. If these variance-covariance matrices are not known, their consistent estimates can be used as well such that the large sample properties of the method remain unchangeable. This approach allows to improve statistical properties of many standard estimators such as an empirical cumulative distribution function, empirical characteristic function, and Nelson-Aalen cumulative hazard estimator.
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Citations
Estimands and their Estimators for Clinical Trials Impacted by the COVID-19 Pandemic: A Report from the NISS Ingram Olkin Forum Series on Unplanned Clinical Trial Disruptions
Kelly Van Lancker,Sergey Tarima,Jonathan Bartlett,Madeline Bauer,Bharani Bharani-Dharan,Frank Bretz,Nancy Flournoy,Hege Michiels,Camila Olarte Parra,James L. Rosenberger,Suzie Cro +10 more
TL;DR: In this paper , the authors demonstrate how the ICH E9(R1) Addendum on estimands and sensitivity analyses provides a rigorous basis to discuss potential pandemic-related trial disruptions and embed these disruptions in the context of study objectives and design elements.
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Characterization of regional hydrological drought using improved precipitation records under multi-auxiliary information
Zulfiqar Ali,Ijaz Hussain,Muhammad Faisal,Muhammad Faisal,Marco Grzegorczyk,Ibrahim M. Almanjahie,Amna Nazeer,Ishfaq Ahmad,Ishfaq Ahmad +8 more
TL;DR: In this article, the authors provided a novel method to improve annual average time series data for the Standardized Drought Index (SDI)-type drought monitoring tools and proposed multi-auxiliary information-based estimation strategy that improves annual moving average/total precipitation time series records.
Nonparametric estimators of probability characteristics using unbiased prior conditions
Yury Glebovich Dmitriev,Gennady M. Koshkin +1 more
- 12 Sep 2018
TL;DR: It is shown that the knowledge usage of other distribution functionals in estimation of the main functional can often provide the mean squared error smaller than that of estimators constructed without such auxiliary information.
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Robust Mean Estimation Under a Possibly Incorrect Log-Normality Assumption
TL;DR: Simulation examples focus on mean estimation when data may follow a lognormal distribution, or can be a mixture with an exponential or a uniform distribution, and for large sample sizes has a smaller mean squared error.
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Estimating the net premium using additional information about a quantile of the cumulative distribution function
TL;DR: Zhanna N. Zenkova and Elizaveta A. Krainova as discussed by the authors proposed a modified estimation of mean value using additional information about the quantile which is unbiased and its variance is asymptotically less than the variance of the classical sample mean, so that the mean square error of the modification is also smaller.
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