Resumen de Robust estimation and forecasting for beta-mixed hierarchical models of grouped binaria data

Yurij S. Kharin, Maxim Pashkevich

• català

  L'article desenvolupa t`ecniques d'estimaci¿o i predicci¿o robusta per a dades bin`aries agrupades quan hi ha respostes classificades malament. Les dades es descriuen mitjan¿cant un model jer`arquic, b¿e el beta-binomial o b¿e el beta-log¿istic, mentre que les males classificacions estan causades per les distorsions estoc`astiques additives de les observacions bin`aries. Per a aquests models, s'avalua l'efecte d'ignorar la mala classificaci¿o i es donen expressions per als biaixos dels estimadors obtinguts pel m`etode dels moments i per la m`axima versemblan¿ca. Tamb¿e es donen expressions per a l'augment de l'error de predicci¿o, en mitjana quadr`atica, dels predictors de Bayes. Per compensar els efectes de la mala classificaci¿o, es construeixen nous estimadors consistents i un nou predictor de Bayes que tenen en compte la distorsi¿o en el model. La robustesa de les t`ecniques desenvolupades es demostra mitjan¿cant simulacions i l'estudi d'un cas real.

• English

  The paper focuses on robust estimation and forecasting techniques for grouped binary data with misclassified responses. It is assumed that the data are described by the beta-mixed hierarchical model (the beta-binomial or the beta-logistic), while the misclassifications are caused by the stochastic additive distortions of binary observations. For these models, the effect of ignoring the misclassifications is evaluated and expressions for the biases of the method-of-moments estimators and maximum likelihood estimators, as well as expressions for the increase in the mean square error of forecasting for the Bayes predictor are given. To compensate the misclassification effects, new consistent estimators and a new Bayes predictor, which take into account the distortion model, are constructed. The robustness of the developed techniques is demonstrated via computer simulations and a real-life case study.