Nonlinear smoothers in two dimensions for environmental data

We present smoothing as an exploratory tool in data analysis, with an emphasis on nonlinear smoothers. Beginning with an underlying model which motivates the need for smoothing, we describe the goals of smoothing and characteristics of good smoothers. We also relate smoothing to the concepts of general fitting, parametric and nonparametric regression, and focus on smoothing two-dimensional data sets such as those that occur with environmental data. To overcome the shortcomings in classical linear smoothers, we propose a nonlinear smoother and demonstrate its performance via simulation. Throughout the article, we illustrate our proposal using data on temperature trends at various monitoring stations across the United States.