What is nonparametric regression and how does it compare to other types of regression models?

1 Parametric vs nonparametric regression

Parametric regression models, such as linear regression or logistic regression, specify a fixed form of the regression function, such as a linear or logistic function, and estimate the unknown parameters using the data. Nonparametric regression models, on the other hand, do not impose any predefined structure on the regression function, and let the data determine its shape. Nonparametric regression models can capture complex and nonlinear patterns in the data, and adapt to different levels of variability across the range of the explanatory variables.

2 Types of nonparametric regression

Nonparametric regression is a type of regression analysis where the regression function is estimated from the data without making any assumptions about the functional form of the model. Popular methods for performing nonparametric regression include kernel regression, spline regression, local polynomial regression, regression trees, and k-nearest neighbors regression. Kernel regression uses a weighted average of nearby observations to estimate the function at each point, while spline regression uses piecewise polynomial functions joined at knots. Local polynomial regression combines kernel and spline techniques, while regression trees partition the data into smaller regions and assign constant values as estimates. Finally, k-nearest neighbors regression uses the average of the k closest observations to estimate the function at each point.

4 Challenges of nonparametric regression

Nonparametric regression has some challenges and limitations that must be addressed, such as needing more data and computational resources than parametric models, as well as suffering from the curse of dimensionality. This means that the performance and efficiency of the method decreases with the number of explanatory variables. Additionally, the method can be sensitive to the choice of smoothing or tuning parameters, such as the bandwidth or k. These parameters must be selected carefully with criteria such as cross-validation. Lastly, interpreting and communicating the results of nonparametric regression can be difficult, as the regression function may not have a simple form and may not provide easily understandable coefficients or measures of significance or confidence.

5 Applications of nonparametric regression

Nonparametric regression is a powerful tool with many applications across various fields and domains. For instance, in economics and finance, it can be used to model demand and supply functions, production and cost functions, income and consumption functions, or asset pricing and return functions without restrictive assumptions. In biology and medicine, it can be employed to model growth and survival curves, dose-response and toxicity curves, gene expression and regulation functions, or disease and treatment effects without relying on parametric models. Additionally, in engineering and physical sciences, nonparametric regression is useful for modeling stress and strain functions, temperature and pressure functions, signal and noise functions, or input and output functions without resorting to parametric models that may not account for nonlinearities or complexities of the systems or phenomena.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?