sharpData (version 1.2)

LLmono: Monotonized Local Linear Regression

Description

Locally linear regression is applied to bivariate data. The response is `sharpened' or perturbed in a way to render a monotonically increasing curve estimate.

Usage

LLmono(x, y, h, xgrid, numgrid = 401, kernel="biweight", call.plot = 
TRUE, ...)

Arguments

x

a vector of explanatory variable observations

y

binary vector of responses

h

bandwidth

xgrid

gridpoints on x-axis where estimates are taken

numgrid

number of equally-spaced gridpoints (if xgrid not specified)

kernel

character constant

call.plot

if TRUE (default), the data, sharpened data and estimated curve are plotted.

...

other arguments for plot

Value

x

original explanatory variable

y

original responses

ysharp

sharpened responses

h

bandwidth

xgrid

gridpoints

ygrid

sharpened curve estimate

Details

Data are perturbed the smallest possible L2 distance subject to the constraint that the local linear estimate is monotonically increasing.

References

Braun, W.J. and Hall, P., Data Sharpening for Nonparametric Estimation Subject to Constraints, Journal of Computational and Graphical Statistics, 2001

Examples

# NOT RUN {
gridpts <- seq(1, 10, length=101)
x <- seq(1, 10, length=51)
p <- exp(-1 + .2*x)/(1 + exp(-1 + .2*x))
y <- rbinom(51, 1, p)
LLmono(x, y, h=0.6, xgrid=gridpts)
lines(x,p) # true mean response
# }