Two strategies are suggested in order to restrict the size of the learning sample taken into account for the estimation of the parameters of the polynomial: Moving window and k nearest neighbors. The polynomial degree used when fitting the model to the observations of the learning sample.It is involved in calculating the kernel and the weights of the observations, and differentiates or rescales the relative weights of the variables while at the same time reducing or augmenting the impact of observations of the learning sample, depending on how far they are from the observation to predict. The bandwidth associated to each variable.The kernel functions available in XLSTAT are: The use of a kernel function, to weigh the observations of the learning sample, depending on their "distance" from the predicted observation. The characteristics of Kernel Regression are: Lastly, the model can be applied to a prediction sample of size npred, for which the values of the dependent variable Y are unknown. A sample of size nvalid can then be used to evaluate the quality of the model. There are many variations of Kernel regression in existence.Īs with any modeling method, a learning sample of size nlearn is used to estimate the parameters of the model. The structure of the model is variable and complex, the latter working like a filter or black box. Unlike linear regression which is both used to explain phenomena and for prediction (understanding a phenomenon to be able to predict it afterwards), Kernel regression is mostly used for prediction. Kernel regression is a modeling tool which belongs to the family of smoothing methods. XLSTAT offers two types of nonparametric regressions: Kernel and Lowess. Nonparametric regression can be used when the hypotheses about more classical regression methods, such as linear regression, cannot be verified or when we are mainly interested in only the predictive quality of the model and not its structure.
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