Electronic Thesis and Dissertation Repository


Doctor of Philosophy


Statistics and Actuarial Sciences


Dr. Ricardas Zitikis


Numerous problems in econometrics, insurance, reliability engineering, and statistics rely on the assumption that certain functions are monotonic, which may or may not be true in real life scenarios. To satisfy this requirement, from the theoretical point of view, researchers frequently model the underlying phenomena using parametric and semi-parametric families of functions, thus effectively specifying the required shapes of the functions. To tackle these problems in a non-parametric way, when the shape cannot be specified explicitly but only estimated approximately, we suggest indices for measuring the lack of monotonicity in functions. We investigate properties of these indices and offer convenient computational techniques for practical use. To illustrate the new technique, we analyze a data-set of student marks on mathematics, reading and spelling. In particular, we apply our technique to determine if the marks are co-monotonic, but if not, then how much they deviate from the co-monotonic pattern. This illustrative example is for convenience only, as our technique is applicable very widely. Indeed, measuring the lack of co-monotonicity between variables plays an important role in a great variety of research areas, as noted at the beginning of this abstract.