Monotonic Regression for Assessment of Trends in Environmental Quality Data

Monotonic regression is a non-parametric method that is designed especially for applications in which the expected value of a response variable increases or decreases in one or more explanatory variables. Here, we show how the recently developed generalised pooladjacent-violators (GPAV) algorithm can greatly facilitate the assessment of trends in time series of environmental quality data. In particular, we present new methods for simultaneous extraction of a monotonic trend and seasonal components and for normalisation of environmental quality data that are influenced by random variation in weather conditions or other forms of natural variability. The general aim of normalisation is to clarify the human impact on the environment by suppressing irrelevant variation in the collected data. Our method is designed for applications that satisfy the following conditions: (i) the response variable under consideration is a monotonic function of one or more covariates; (ii) the anthropogenic temporal trend is either increasing or decreasing; (iii) the seasonal variation over a year can be defined by one increasing and one decreasing function. Theoretical descriptions of our methodology are accompanied by examples of trend assessments of water quality data and normalisation of the mercury concentration in cod muscle in relation to the length of the analysed fish. Mohamed Hussian, Anders Grimvall, Oleg Burdakov, Oleg Sysoev 2