Prediction of a function of misclassified binary data

Noriah M.  Al-Kandari; Partha  Lahiri

doi:https://doi.org/10.59170/stattrans-2016-025

Prediction of a function of misclassified binary data

Noriah M. Al-Kandari Department of Statistics and Operations Research, Kuwait University. , Partha Lahiri Joint Program in Survey Methodology, University of Maryland. Statistics in Transition new series, vol. 17, 2016, 3, pages: 429-447 Published online: 1 September 2016 https://doi.org/10.59170/stattrans-2016-025

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ABSTRACT

We consider the problem of predicting a function of misclassified binary variables. We make an interesting observation that the naive predictor, which ignores the misclassification errors, is unbiased even if the total misclassification error is high as long as the probabilities of false positives and false negatives are identical. Other than this case, the bias of the naive predictor depends on the misclassification distribution and the magnitude of the bias can be high in certain cases. We correct the bias of the naive predictor using a double sampling idea where both inaccurate and accurate measurements are taken on the binary variable for all the units of a sample drawn from the original data using a probability sampling scheme. Using this additional information and design-based sample survey theory, we derive a biascorrected predictor. We examine the cases where the new bias-corrected predictors can also improve over the naive predictor in terms of mean square error (MSE).

KEYWORDS

binary classification, double sampling, finite population sampling, misclassification, linkage error, sampling design

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