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 bias and improve accuracy near the edges of the domain. Kernel choices such as Gaussian, Epanechnikov, or uniform affect efficiency but not the overall consistency under standard regularity conditions.

Bandwidth selection is a central practical consideration, as it governs the bias-variance trade-off. Common approaches include cross-validation, plugin selectors, and rule-of-thumb methods. Diagnostic plots and out-of-sample tests help assess the quality of the fit.

Advantages of kernelregressie include flexibility and minimal structural assumptions, making it suitable for uncovering nonlinear relationships and for exploratory analysis. Limitations include sensitivity to the choice of bandwidth and kernel, higher data requirements, and the curse of dimensionality in multivariate settings. Computational demands increase with dataset size, though efficient algorithms exist for one-dimensional inputs.

Kernelregressie is related to other kernel smoothing and nonparametric regression techniques and is widely used in econometrics, environmental science, and finance for estimating conditional expectations, demand curves, and other relationships where parametric models are inadequate.