G M van Kempen1, L J van Vliet. 1. Central Analytical Sciences, Unilever Research Vlaardingen, Vlaardingen, The Netherlands. geert-van.kempen@unilever.com
Abstract
BACKGROUND: The ratio of two measured fluorescence signals (called x and y) is used in different applications in fluorescence microscopy. Multiple instances of both signals can be combined in different ways to construct different ratio estimators. METHODS: The mean and variance of three estimators for the ratio between two random variables, x and y, are discussed. Given n samples of x and y, we can intuitively construct two different estimators: the mean of the ratio of each x and y and the ratio between the mean of x and the mean of y. The former is biased and the latter is only asymptotically unbiased. Using the statistical characteristics of this estimator, a third, unbiased estimator can be constructed. RESULTS: We tested the three estimators on simulated data, real-world fluorescence test images, and comparative genome hybridization (CGH) data. The results on the simulated and real-world test images confirm the presented theory. The CGH experiments show that our new estimator performs better than the existing estimators. CONCLUSIONS: We have derived an unbiased ratio estimator that outperforms intuitive ratio estimators. Copyright 2000 Wiley-Liss, Inc.
BACKGROUND: The ratio of two measured fluorescence signals (called x and y) is used in different applications in fluorescence microscopy. Multiple instances of both signals can be combined in different ways to construct different ratio estimators. METHODS: The mean and variance of three estimators for the ratio between two random variables, x and y, are discussed. Given n samples of x and y, we can intuitively construct two different estimators: the mean of the ratio of each x and y and the ratio between the mean of x and the mean of y. The former is biased and the latter is only asymptotically unbiased. Using the statistical characteristics of this estimator, a third, unbiased estimator can be constructed. RESULTS: We tested the three estimators on simulated data, real-world fluorescence test images, and comparative genome hybridization (CGH) data. The results on the simulated and real-world test images confirm the presented theory. The CGH experiments show that our new estimator performs better than the existing estimators. CONCLUSIONS: We have derived an unbiased ratio estimator that outperforms intuitive ratio estimators. Copyright 2000 Wiley-Liss, Inc.
Authors: Robert J Freishtat; Lindsay W Mitchell; Svetlana D Ghimbovschi; Samuel B Meyers; Eric P Hoffman Journal: Hum Immunol Date: 2006-03-27 Impact factor: 2.850
Authors: Renato Filogonio; Antônio V G S Neto; Mariana M Zamponi; Augusto S Abe; Cléo A C Leite Journal: J Comp Physiol B Date: 2021-08-07 Impact factor: 2.200
Authors: Mary Ann Checkley; Kunio Nagashima; Stephen J Lockett; Katherine M Nyswaner; David J Garfinkel Journal: Mol Cell Biol Date: 2009-11-09 Impact factor: 4.272
Authors: Warren P Voth; Yaxin Yu; Shinya Takahata; Kelsi L Kretschmann; Jason D Lieb; Rebecca L Parker; Brett Milash; David J Stillman Journal: EMBO J Date: 2007-09-27 Impact factor: 11.598