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Profiting from correlations: Adjusted estimators for categorical data
Author(s) -
Niebuhr Tobias,
Trabs Mathias
Publication year - 2019
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2452
Subject(s) - estimator , categorical variable , skewness , weighting , contingency table , statistics , econometrics , marginal distribution , variance (accounting) , sample (material) , mathematics , computer science , economics , random variable , medicine , chemistry , accounting , chromatography , radiology
To take sample biases and skewness in the observations into account, practitioners frequently weight their observations according to some marginal distribution. The present paper demonstrates that such weighting can indeed improve the estimation. Studying contingency tables, estimators for marginal distributions are proposed under the assumption that another marginal is known. It is shown that the weighted estimators have a strictly smaller asymptotic variance whenever the two marginals are correlated. The finite sample performance is illustrated in a simulation study. As an application to traffic accident data the method allows for correcting a well‐known bias in the observed injury severity distribution.