Locally-weighted regression (skmisc.loess)

Loess is a procedure for estimating a regression surface by a multivariate smoothing procedure. A linear or quadratic function of the independent variables is fit in a moving fashion that is analogous to how a moving average is computed for a time series.

Compared to approaches that fit global parametric functions, loess substantially increases the domain of surfaces that can be estimated without distortion. However, analogues of the statistical procedures used in parametric function fitting – for example, ANOVA and t intervals – involve statistics whose distributions are well approximated by familiar distributions.

loess(x, y[, weights])

Locally-weighted regression

loess_inputs(x, y[, weights])

Initialization class for loess data inputs

loess_model(p[, family, span, degree, ...])

Initialization class for loess fitting parameters

loess_control([surface, statistics, ...])

Initialization class for loess control parameters

loess_outputs(n, p, family)

Class of a loess fit outputs

loess_prediction(newdata, loess[, stderror])

Class for loess prediction results

loess_confidence_intervals(pred, alpha)

Pointwise confidence intervals of a loess-predicted object

loess_anova(loess_one, loess_two)

Analysis of variance for two loess objects


The original source code was written by William S. Cleveland, Eric Grosse and Ming-Jen Shyu. It is available at http://www.netlib.org/a/dloess. It was initially adapted to for use in Scipy by Pierre GF Gerard-Marchant.

For more see references [1] [2] and [3].


W. S. Cleveland, E. Grosse, and M. J. Shyu. Local Regression Models. In J. M. Chambers and T. Hastie, editors, Statistical Models in S, pages 309–376. Chapman and Hall, New York, 1992.


W. S. Cleveland, S. J. Devlin, and E. Grosse. Regression by Local Fitting: Methods, Properties, and Computing. Journal of Econometrics, 37: pp. 87–114. 1988.


W. S. Cleveland. Robust Locally Weighted Regression and Smoothing Scatterplots. Journal of the American Statistical Association, 74: pp. 829–836. 1979.