Improper Multivariate Receiver Operating Characteristic (iMROC) Curve

In a multivariate setup, the classification techniques have its significance in identifying the exact status of the individual/observer along with accuracy of the test. One such classification technique is the Multivariate Receiver Operating Characteristic (MROC) Curve. This technique is well known to explain the extent of correct classification with the curve above the random classifier (guessing line) when it satisfies all of its properties especially the property of increasing likelihood ratio function. However, there are circumstances where the curve violates the above property. Such a curve is termed as improper curve. This paper demonstrates the methodology of improperness of the MROC Curve and ways of measuring it. The methodology is explained using real data sets.