Quantification of the environmental structural risk with spoiling ties: Is randomization worthwhile?

Many recent works show that copulas turn out to be useful in a variety of different applications, especially in environmental sciences. Here the variables of interest are usually continuous, being times, lengths, weights, and so on. Unfortunately, the corresponding observations may suffer from (instrumental) adjustments and truncations, and eventually may show several repeated values (i.e., ties). In turn, on the one hand, a tricky issue of identifiability of the model arises, and, on the other hand, the assessment of the risk may be adversely affected. A possible remedy is to adopt suitable randomization procedures: here three diffe ent strategies are outlined. The goal of the work is to carry out a simulation study in order to evaluate the effects of the randomization of multivariate observations when ties are present. In particular, it will be investigated whether, how, and to what extent, the randomization may change the estimation of the structural risk: for this purpose, a coastal engineering example will be used, as archetypical of a broad class of models and problems in engineering applications. Practical advices and warnings about the use of randomization techniques are hence given.