方法对比

	广义可加模型位置、尺度和形状（GAMLSS）	广义可加模型 (GAM)	分位数回归
领域	统计学	机器学习	计量经济学
方法族	Regression model	Machine learning	Regression model
起源年份	2005	1986	1978
提出者	Robert Rigby & Mikis Stasinopoulos	Trevor Hastie & Robert Tibshirani	Koenker & Bassett
类型	Semi-parametric distributional regression model	Semi-parametric additive regression model	Conditional quantile regression
开创性文献	Rigby, R. A., & Stasinopoulos, D. M. (2005). Generalized additive models for location, scale and shape. Journal of the Royal Statistical Society: Series C, 54(3), 507–554.	Hastie, T., & Tibshirani, R. (1986). Generalized additive models. Statistical Science, 1(3), 297–310.	Koenker, R. & Bassett, G., Jr. (1978). Regression Quantiles. Econometrica, 46(1), 33-50.
别名	Distributional Regression, Flexible Regression and Smoothing, GAMLSS Framework, Konum, Ölçek ve Şekil için Genelleştirilmiş Toplamlı Modeller	GAM, additive model, spline-based additive regression, Genelleştirilmiş toplamsal model	conditional quantile regression, regression quantiles, Kantil Regresyon
相关	2	4	5
摘要	GAMLSS is a broad class of semi-parametric regression models introduced by Robert Rigby and Mikis Stasinopoulos in 2005. Unlike classical regression, which models only the mean of a response, GAMLSS allows each parameter of a chosen parametric distribution — location (e.g., mean), scale (e.g., variance), and shape (e.g., skewness, kurtosis) — to be modeled as an additive function of covariates. This makes it possible to capture heteroscedasticity, skewness, and heavy tails simultaneously within a single unified framework.	A generalized additive model, introduced by Trevor Hastie and Robert Tibshirani in 1986, extends the generalized linear model by replacing each linear term with a smooth, data-driven function of the predictor. This lets the model capture nonlinear relationships while preserving the additive, term-by-term interpretability of regression: each predictor contributes its own estimated curve, and the curves simply add up (on a link scale) to predict the response.	Quantile regression models conditional quantiles of an outcome - the median, the 25th or 75th percentile, and so on - rather than the conditional mean that OLS targets. Introduced by Koenker and Bassett in 1978, it reveals how predictors act across the whole distribution, including its tails.