kernelregressie
Kernelregressie is a nonparametric regression technique used to estimate the conditional mean function m(x) = E[Y|X = x] without assuming a specific parametric form. It relies on kernel smoothing to weight observations by their proximity to x, controlled by a bandwidth parameter h and a kernel function K. The most common form is the Nadaraya-Watson estimator: m_hat(x) = sum_i K((x - x_i)/h) y_i divided by sum_i K((x - x_i)/h). This produces a smooth curve that adapts to local patterns in the data.
Variations include locally linear regression, which fits a linear model locally around x to reduce boundary
Bandwidth selection is a central practical consideration, as it governs the bias-variance trade-off. Common approaches include
Advantages of kernelregressie include flexibility and minimal structural assumptions, making it suitable for uncovering nonlinear relationships
Kernelregressie is related to other kernel smoothing and nonparametric regression techniques and is widely used in