2016/11/21 by Arindam Chatterjee, Chatterjee, Arindam, Tathagata Bandyopadhyay +3
Mathematics · #62F12 #62F40 #62J12 #Advanced Statistical Methods and Models #FOS: Mathematics #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST) #Survey Sampling and Estimation Techniques
paper · pdf · doi:10.48550/arxiv.1611.06727
openalex publication_date 2016/11/21 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
Misclassification of binary responses, if ignored, may severely bias the\nmaximum likelihood estimators (MLE) of regression parameters. For such data, a\nbinary regression model incorporating misclassification probabilities is\nextensively used by researchers in different application contexts. The model,\nhowever, suffers from a serious estimation problem because of confounding of\nthe unknown misclassification probabilities with the regression parameters. To\novercome this problem, in addition to the main sample, use of internal\nvalidation data is proposed. However, the maximum likelihood estimators (MLE)\nare found to be substantially biased. Investigating further, we propose a\nmaximum pseudo-likelihood method of estimation which leads to bias reduction.\nFor drawing inference on the regression parameters, we develop a rigorous\nasymptotic theory for the maximum pseudo-likelihood estimators under standard\nassumptions. To facilitate its easy implementation, a bootstrapped version of\nthe estimator is proposed, and its distributional consistency is proved.\nExtensions of these results are also provided for more general\nmisclassification models. The results of the simulation studies are\nencouraging. The methodology is illustrated with a survey data.\n