Prediction of a Function of Misclassified Binary Data
Prediction of a Function of Misclassified Binary Data

Summary/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 misclassificationerrors, is unbiased even if the total misclassification error is high aslong as the probabilities of false positives and false negatives are identical. Otherthan this case, the bias of the naive predictor depends on the misclassification distributionand the magnitude of the bias can be high in certain cases. We correct thebias of the naive predictor using a double sampling idea where both inaccurate andaccurate measurements are taken on the binary variable for all the units of a sampledrawn from the original data using a probability sampling scheme. Using thisadditional information and design-based sample survey theory, we derive a biascorrectedpredictor. We examine the cases where the new bias-corrected predictorscan also improve over the naive predictor in terms of mean square error (MSE).

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