Calculating Kendall's Tau with multiple measurements

Relationships between time series of environmental variables are commonly calculated using non-parametric methods, such as Kendall’s τ, because of ”non-detects”, i.e., left-censored data that falls below a measurement limit. However, these methods are not well-adapted to situations where variables have multiple contemporaneous measurements. In this thesis, we define a new method, τ ̃, in an attempt to calculate correlations using each of the multiple measurements instead of daily means. We investigate τ ̃ using two methods: simulations that approximate a null distribution for τ ̃ and closed form calculations for a specific special case. We also apply τ ̃ to an actual data set. The results of our investigation shows that τ ̃ may handle certain things, such as outliers, better than current methods. However, its requirements for distributional assumptions about the data make it a less practical option for real data. Further work could explore ways to avoid the prerequisite need for distribution knowledge and could also further investigate τ ̃ under noise sampled from asymmetric distributions.