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Nonparametric and semiparametric regression

10 articles

Additive model

The Additive model is a regression technique where the effect of each predictor is the sum of its separate contributions. It is a core structure of Generalized Additive Models (GAMs).

Additive regression

Additive regression is a nonparametric regression method that models a response as a sum of smooth functions of individual predictors, keeping linear-model interpretability while learning curved relationships.

Classification and regression tree

Classification and regression trees (CART) is a decision-tree method that predicts outcomes by recursively splitting data, using the Gini index for classification and squared residuals for regression.

Conditional density estimation

Conditional density estimation (CDE) is the statistical task of estimating the full conditional density p(y|x) from data, supplying modes, prediction intervals, and samples that ordinary regression cannot.

Fréchet regression

Fréchet regression is a statistical method for regressing random objects, such as probability distributions, covariance matrices, or shapes, on Euclidean predictors, introduced by Petersen and Müller in 2019.

Isotonic regression

Isotonic regression is a nonparametric method that fits a nondecreasing function to ordered data by minimizing weighted squared error, used for probability calibration and dose-response estimation.

Kernel regression

Kernel regression is a nonparametric method for estimating a regression function from data without a fixed parametric form, using weighted averages such as the Nadaraya–Watson estimator.

Rank regression

Rank regression is a nonparametric regression method that fits models to the ranks of the data instead of raw values, reducing sensitivity to outliers and distributional assumptions.

Recursive partitioning

Recursive partitioning is a statistical method that builds classification and regression models by repeatedly splitting a dataset into smaller subgroups, producing a binary tree whose leaves carry predictions.

Varying coefficient model

A varying coefficient model is a regression method where coefficients vary smoothly with a covariate such as time, credited to Hastie and Tibshirani's 1993 paper.