Nonparametric regression

Nonparametric regression

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


Kernel regression

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.

Nonparametric multiplicative regression

Nonparametric multiplicative regression (NPMR) is a form of nonparametric regression based on multiplicative kernel estimation. This is a smoothing technique that can be cross-validated and applied in a predictive way. Many other smoothing techniques are well known, for example smoothing splines and wavelets. Optimum choice of a smoothing method depends on the specific application. NPMR is useful for habitat modeling. The multidimensionality is provided multiplicatively – this automatically and parsimoniously models the complex interactions among predictors in much the same way that organisms integrate the numerous factors affecting their performance.[1] Optimizing the selection of predictors and their smoothing parameters in a multiplicative model is computationally intensive. NPMR can be applied to either presence-absence or quantitative response data, with either categorical or quantitative predictors.

NPMR can be applied with a local mean estimator, a local linear estimator, or a local logistic estimator. In each case the weights can be extended multiplicatively to m dimensions. In words, the estimate of the response is a local estimate (for example a local mean) of the observed values, each value weighted by its proximity to the target point in the predictor space, the weights being the product of weights for individual predictors. The model allows interactions, because weights for individual predictors are combined by multiplication rather than addition. A key biological feature of the model is that failure of a population with respect to any single dimension of the predictor space results in failure at that point, because the product of the weights for the point is zero or near zero if any of the individual weights are zero or near zero.

Regression trees

Decision tree learning algorithms can be applied to learn to predict a dependent variable from data.[2] Although the original CART formulation applied only to predicting univariate data, the framework can be used to predict multivariate data including time series.[3]

See also


  1. ^ McCune, B. (2006), "Non-parametric habitat models with automatic interactions", Journal of Vegetation Science 17 (6): 819–830, doi:10.1658/1100-9233(2006)17[819:NHMWAI]2.0.CO;2. 
  2. ^ Breiman, Leo; Friedman, J. H., Olshen, R. A., & Stone, C. J. (1984), Classification and regression trees, Monterey, CA: Wadsworth & Brooks/Cole Advanced Books & Software, ISBN 978-0412048418 
  3. ^ Segal, M.R. (1992), "Tree-structured methods for longitudinal data", Journal of the American Statistical Association 87 (418): 407–418, doi:10.2307/2290271, JSTOR 2290271 
  • McCune, B. and M. J. Mefford. 2004. HyperNiche. Nonparametric Multiplicative Habitat Modeling. MjM Software, Gleneden Beach, Oregon, U.S.A.

External links

Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Regression analysis — In statistics, regression analysis is a collective name for techniques for the modeling and analysis of numerical data consisting of values of a dependent variable (response variable) and of one or more independent variables (explanatory… …   Wikipedia

  • Régression non paramétrique — La régression non paramétrique est une forme d analyse de la régression dans lequel le predicteur ne prend pas de forme prédéterminée, mais est construit selon les informations provenant des données. La régression non paramétrique exige des… …   Wikipédia en Français

  • Regression toward the mean — In statistics, regression toward the mean (also known as regression to the mean) is the phenomenon that if a variable is extreme on its first measurement, it will tend to be closer to the average on a second measurement, and a fact that may… …   Wikipedia

  • Regression discontinuity design — In statistics, econometrics, epidemiology and related disciplines, a regression discontinuity design (RDD) is a design that elicits the causal effects of interventions by exploiting a given exogenous threshold determining assignment to treatment …   Wikipedia

  • Linear regression — Example of simple linear regression, which has one independent variable In statistics, linear regression is an approach to modeling the relationship between a scalar variable y and one or more explanatory variables denoted X. The case of one… …   Wikipedia

  • Kernel regression — Not to be confused with Kernel principal component analysis. The kernel regression is a non parametric technique in statistics to estimate the conditional expectation of a random variable. The objective is to find a non linear relation between a… …   Wikipedia

  • Outline of regression analysis — In statistics, regression analysis includes any technique for learning about the relationship between one or more dependent variables Y and one or more independent variables X. The following outline is an overview and guide to the variety of… …   Wikipedia

  • Robust regression — In robust statistics, robust regression is a form of regression analysis designed to circumvent some limitations of traditional parametric and non parametric methods. Regression analysis seeks to find the effect of one or more independent… …   Wikipedia

  • Nonlinear regression — See Michaelis Menten kinetics for details In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or… …   Wikipedia

  • Kernel-Regression — Unter Kernel Regression versteht man eine Reihe nichtparametrischer statistischer Methoden, bei denen die Abhängigkeit einer zufälligen Größe von Ausgangsdaten mittels Kerndichteschätzung geschätzt werden. Die Art der Abhängigkeit, dargestellt… …   Deutsch Wikipedia