fence.NF: Fence model selection (Nonparametric Model)
In fence: Using Fence Methods for Model Selection

Description Usage Arguments Value Author(s) References Examples

Fence model selection (Noparametric Model)

1 2	fence.NF(full, data, spline, ps = 1:3, qs = NA, B = 100, grid = 101, bandwidth = NA, lambda)

`full`	formula of full model
`data`	data
`spline`	variable needed for spline terms
`ps`	order of power
`qs`	number of knots
`B`	number of bootstrap sample, parametric for lmer
`grid`	grid for c
`bandwidth`	bandwidth for kernel smooth function
`lambda`	A grid of lambda values

`models`	list all model candidates with p polynomial degrees and q knots in the model space
`Qd_matrix`	list a matrix of QM - QM.tilde for all model candidates. Each row is for each bootrap sample
`bandwidth`	list the value of bandwidth
`model_mat`	list a matrix of selected models at each c values in grid (in columns). Each row is for each bootstrap sample
`freq_mat`	list a matrix of coverage probabilities (frequency/smooth_frequency) of each selected models for a given c value (index)
`c`	list the adaptive choice of c value from which the parsimonious model is selected
`lambda`	penalty (or smoothing) parameter estimate given selected p and q
`sel_model`	list the selected (parsimonious) model given the adaptive c value
`beta.est.u`	A list of coefficient estimates given a lambda value
`f.x.hat`	A vector of fitted values obtained from a given lambda value and beta.est.u

@note The current Fence method in Nonparametric model focuses on one spline variable. This method can be extended to a general case with more than one spline variables, and includes non-spline variables.

Jiming Jiang Jianyang Zhao J. Sunil Rao Bao-Qui Tran Thuan Nguyen

Jiang J., Rao J.S., Gu Z., Nguyen T. (2008), Fence Methods for Mixed Model Selection. The Annals of Statistics, 36(4): 1669-1692
Jiang J., Nguyen T., Rao J.S. (2009), A Simplified Adaptive Fence Procedure. Statistics and Probability Letters, 79, 625-629
Jiang J., Nguyen T., Rao J.S. (2010), Fence Method for Nonparametric Small Area Estimation. Survey Methodology, 36, 1, 3-11

## Not run: 
require(fence)
n = 100
set.seed(1234)
x=runif(n,0,3)
y = 1-x+x^2- 2*(x-1)^2*(x>1) + 2*(x-2)^2*(x>2) + rnorm(n,sd=.2)
lambda=exp((c(1:60)-30)/3)
data=data.frame(cbind(x,y))   
test_NF = fence.NF(full=y~x, data=data, spline='x', ps=c(1:3), qs=c(2,5), B=1000, lambda=lambda)
plot(test_NF)
summary <- summary(test_NF) 
model_sel <- summary[[1]]
model_sel
lambda_sel <- summary[[2]]
lambda_sel

## End(Not run)