fANCOVA (version 0.5-1)

loess.as: Fit a local polynomial regression with automatic smoothing parameter selection

Description

Fit a local polynomial regression with automatic smoothing parameter selection. Two methods are available for the selection of the smoothing parameter: bias-corrected Akaike information criterion (aicc); and generalized cross-validation (gcv).

Usage

loess.as(x, y, degree = 1, criterion = c("aicc", "gcv"), 
		family = c("gaussian", "symmetric"), user.span = NULL, 
		plot = FALSE, ...)

Arguments

x

a vector or two-column matrix of covariate values.

y

a vector of response values.

degree

the degree of the local polynomials to be used. It can ben 0, 1 or 2.

criterion

the criterion for automatic smoothing parameter selection: ``aicc'' denotes bias-corrected AIC criterion, ``gcv'' denotes generalized cross-validation.

family

if ``gaussian'' fitting is by least-squares, and if ``symmetric'' a re-descending M estimator is used with Tukey's biweight function.

user.span

the user-defined parameter which controls the degree of smoothing.

plot

if TRUE, the fitted curve or surface will be generated.

…

control parameters.

Value

An object of class ``loess''.

Details

Fit a local polynomial regression with automatic smoothing parameter selection. The predictor x can either one-dimensional or two-dimensional.

References

Cleveland, W. S. (1979) Robust locally weighted regression and smoothing scatterplots. Journal of the American Statistical Association. 74, 829--836.

Hurvich, C.M., Simonoff, J.S., and Tsai, C.L. (1998), Smoothing Parameter Selection in Nonparametric Regression Using an Improved Akaike Information Criterion. Journal of the Royal Statistical Society B. 60, 271--293.

Golub, G., Heath, M. and Wahba, G. (1979). Generalized cross validation as a method for choosing a good ridge parameter. Technometrics. 21, 215--224.

See Also

loess, loess.ancova, T.L2, T.aov, T.var.

Examples

# NOT RUN {
## Fit Local Polynomial Regression with Automatic Smoothing Parameter Selection
n1 <- 100
x1 <- runif(n1,min=0, max=3)
sd1 <- 0.2
e1 <- rnorm(n1,sd=sd1)
y1 <- sin(2*x1) + e1

(y1.fit <- loess.as(x1, y1, plot=TRUE))

n2 <- 100
x21 <- runif(n2, min=0, max=3)
x22 <- runif(n2, min=0, max=3)
sd2 <- 0.25
e2 <- rnorm(n2, sd=sd2)
y2 <- sin(2*x21) + sin(2*x22) + 1 + e2

(y2.fit <- loess.as(cbind(x21, x22), y2, plot=TRUE))

# }