University of Minnesota
We analyze a dataset on seawater pattern over the last few decades. For specificity, we restrict attention to temperature measures in the Arctic Ocean region for this talk. Our goal is to investigate whether there is a significant change of pattern in the Arctic Ocean seawater temperature, thus detecting climate change, after accounting for the systematic factors like location, depth, season, and the temporal and spatial dependence pattern of the observations. We do not explicitly model the spatio-temporal dependency pattern of the observations, but treat it as an extremely high dimensional nuisance parameter, and use techniques for estimation and inference that are insensitive to it. We use nonparametric curve fitting for weakly dependent observations to model different functions of seawater temperature, and then perform sequential tests to detect whether the function under consideration has changed its pattern from previous time-points. A complex resampling-based robustness study is used to decide whether the changes detected are chance aberrations. Finally, we separate the data in two parts based on observation-time, and use a block bootstrap based scheme to compare temperature patterns in the two regimes. The block-bootstrap based technique elicits probabilities that are the equivalents of size, power and $p$-value of our sequential testing procedure, under reasonable assumptions. The methodology used in this paper is applicable for any sequence of dependent observations on the climate, and unlike many other climate studies does not rely on computer simulated deterministic outputs, nor use of indirect historical data, nor rely on technical assumptions like linearity, Gaussian nature of random variables, specific dependency patterns, and so on. This work is joint done with Qiqi Deng and Jie Xu. This is joint work with Mathieu Ribatet, EPFL, Switzerland.