LOESSLOWESSmenetelmät

LOESS (Locally Estimated Scatterplot Smoothing) and LOWESS (Locally Weighted Scatterplot Smoothing) are non-parametric regression methods used to model the relationship between two variables in a dataset. These methods are particularly useful for visualizing the trend in data that may be nonlinear or have complex patterns.

LOESS and LOWESS are similar techniques that fit simple models to localized subsets of the data to build a function that describes the deterministic part of the variance in the data. The key difference between the two lies in the weighting of data points. In LOESS, the weights are determined using a tricube weight function, while LOWESS uses a bisquare weight function. Both methods involve a smoothing parameter, typically denoted as α (alpha), which determines the proportion of data points used to fit the model at each point.

The process begins by selecting a target point and then choosing a subset of data points within a certain neighborhood around the target. The size of this neighborhood is determined by the smoothing parameter. Weights are then assigned to these data points based on their distance from the target point, with closer points receiving higher weights. A polynomial regression model, usually linear or quadratic, is fitted to the weighted data points. This process is repeated for each point in the dataset to produce a smooth curve that represents the underlying trend.

LOESS and LOWESS are widely used in various fields such as statistics, economics, and environmental science for exploratory data analysis and data visualization. They are particularly useful when the relationship between variables is not well understood or when the data contains outliers or nonlinearities. However, these methods can be computationally intensive, especially for large datasets, and the choice of the smoothing parameter can significantly affect the results.