ibr: Iterative bias reduction multivariate smoothing
- Los Alamos National Laboratory
- AGRO-SUP, FRANCE
- RENNES 2, FRANCE
Regression is a fundamental data analysis tool for relating a univariate response variable Y to a multivariate predictor X {element_of} E R{sup d} from the observations (X{sub i}, Y{sub i}), i = 1,...,n. Traditional nonparametric regression use the assumption that the regression function varies smoothly in the independent variable x to locally estimate the conditional expectation m(x) = E[Y|X = x]. The resulting vector of predicted values {cflx Y}{sub i} at the observed covariates X{sub i} is called a regression smoother, or simply a smoother, because the predicted values {cflx Y}{sub i} are less variable than the original observations Y{sub i}. Linear smoothers are linear in the response variable Y and are operationally written as {cflx m} = X{sub {lambda}}Y, where S{sub {lambda}} is a n x n smoothing matrix. The smoothing matrix S{sub {lambda}} typically depends on a tuning parameter which we denote by {lambda}, and that governs the tradeoff between the smoothness of the estimate and the goodness-of-fit of the smoother to the data by controlling the effective size of the local neighborhood over which the responses are averaged. We parameterize the smoothing matrix such that large values of {lambda} are associated to smoothers that averages over larger neighborhood and produce very smooth curves, while small {lambda} are associated to smoothers that average over smaller neighborhood to produce a more wiggly curve that wants to interpolate the data. The parameter {lambda} is the bandwidth for kernel smoother, the span size for running-mean smoother, bin smoother, and the penalty factor {lambda} for spline smoother.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC52-06NA25396
- OSTI ID:
- 962309
- Report Number(s):
- LA-UR-09-01326; LA-UR-09-1326; TRN: US200919%%71
- Journal Information:
- Journal of Statistical Software, Vol. 55, Issue 2
- Country of Publication:
- United States
- Language:
- English
Similar Records
Stochastic approximation methods for fusion-rule estimation in multiple sensor systems
Multiple sensor fusion under unknown distributions