# Nonparametric regression

**non-parametric regressionnonparametricnon-parametricnon-parametric meansnonparametric estimatorsregression**

Nonparametric regression is a category of regression analysis in which the predictor does not take a predetermined form but is constructed according to information derived from the data.wikipedia

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### Regression analysis

**regressionmultiple regressionregression model**

Nonparametric regression is a category of regression analysis in which the predictor does not take a predetermined form but is constructed according to information derived from the data.

Less common forms of regression use slightly different procedures to estimate alternative location parameters (e.g., quantile regression or Necessary Condition Analysis ) or estimate the conditional expectation across a broader collection of non-linear models (e.g., nonparametric regression).

### Local regression

**LOESSLowess curveLoess curve**

They are two strongly related non-parametric regression methods that combine multiple regression models in a k-nearest-neighbor-based meta-model.

### Multivariate adaptive regression spline

**Multivariate adaptive regression splinesHinge functionsMARS**

It is a non-parametric regression technique and can be seen as an extension of linear models that automatically models nonlinearities and interactions between variables.

### Nonparametric statistics

**non-parametricnon-parametric statisticsnonparametric**

### Semiparametric regression

**regressionsemiparametric modelingsingle and multiple index models**

### Parametric model

**parametricregular parametric modelparameters**

Nonparametric regression requires larger sample sizes than regression based on parametric models because the data must supply the model structure as well as the model estimates.

### Multivariate normal distribution

**multivariate normalbivariate normal distributionjointly normally distributed**

The errors are assumed to have a multivariate normal distribution and the regression curve is estimated by its posterior mode.

### Maximum a posteriori estimation

**maximum a posterioriMAPposterior mode**

The errors are assumed to have a multivariate normal distribution and the regression curve is estimated by its posterior mode.

### Empirical Bayes method

**empirical BayesEmpirical Bayes methodsEmpirical Bayesian**

The Gaussian prior may depend on unknown hyperparameters, which are usually estimated via empirical Bayes.

### Smoothing spline

**smoothing splinesspline smoothingspline**

Smoothing splines have an interpretation as the posterior mode of a Gaussian process regression.

### Convolution

**convolvedconvolvingconvolution kernel**

Kernel regression estimates the continuous dependent variable from a limited set of data points by convolving the data points' locations with a kernel function—approximately speaking, the kernel function specifies how to "blur" the influence of the data points so that their values can be used to predict the value for nearby locations.

### Positive-definite kernel

**kernel functionpositive definitePositive definite kernel**

Kernel regression estimates the continuous dependent variable from a limited set of data points by convolving the data points' locations with a kernel function—approximately speaking, the kernel function specifies how to "blur" the influence of the data points so that their values can be used to predict the value for nearby locations.

### Additive model

In statistics, an additive model (AM) is a nonparametric regression method.

### Nancy E. Heckman

Nancy E. Heckman is a Canadian statistician, interested in nonparametric regression, smoothing, functional data analysis, and applications of statistics in evolutionary biology.

### Variance function

**Variance functions**

It is a main ingredient in the generalized linear model framework and a tool used in non-parametric regression, semiparametric regression and functional data analysis.

### Raymond J. Carroll

**Raymond Carroll**

He has made fundamental contributions to measurement error model, nonparametric and semiparametric modeling.

### Xihong Lin

Xihong Lin is a Chinese-American statistician known for her contributions to mixed models, nonparametric and semiparametric regression, and statistical genetics and genomics.

### Nils Lid Hjort

**Hjort, N.L.Hjort, Nils Lid**

Hjort's research themes are varied, with particularly noteworthy contributions in the fields of Bayesian probability (Beta processes for use in non- and semi-parametric models, particularly within survival analysis and event history analysis, but also with links to Indian buffet processes in machine learning), density estimation and nonparametric regression (local likelihood methodology), and model selection (focused information criteria and model averaging).

### Kernel regression

**kernel ridge regressionnonparametric**

In any nonparametric regression, the conditional expectation of a variable Y relative to a variable X may be written:

### Generalized additive model

**generalised additive model**

The functions f i may be functions with a specified parametric form (for example a polynomial, or an un-penalized regression spline of a variable) or may be specified non-parametrically, or semi-parametrically, simply as 'smooth functions', to be estimated by non-parametric means.

### Forecasting

**forecastforecastsprojection**

### William S. Cleveland

**ClevelandCleveland, William S.**

William Swain Cleveland II (born 1943) is an American computer scientist and Professor of Statistics and Professor of Computer Science at Purdue University, known for his work on data visualization, particularly on nonparametric regression and local regression.

### Interval predictor model

Interval Predictor Models are sometimes referred to as a nonparametric regression technique, because a potentially infinite set of functions are contained by the IPM, and no specific distribution is implied for the regressed variables.

### Richard Samworth

**Samworth, RichardRichard J. Samworth**

Particular topics include shape-constrained density estimation and other nonparametric function estimation problems, nonparametric classification, clustering and regression, the bootstrap and high-dimensional variable selection problems.