sharpData (version 1.4)

Monolpoly: Monotonized Local Regression

Description

Local constant and local linear regression are applied to bivariate data. The response is `sharpened' or perturbed in a way to render a monotonically increasing curve estimate.

Usage

Monolpoly(x, y, h, d=1,  xgrid, numgrid = 401, ...)

Arguments

x

a vector of explanatory variable observations

y

binary vector of responses

h

bandwidth

d

degree, can be either 0 or 1

xgrid

gridpoints on x-axis where monotonicity constraint is enforced

numgrid

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

...

other arguments for locpoly

Value

x

locations of function estimate evaluations

y

function estimate evaluations (sharpened - monotonized)

ysharp

sharpened responses

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)
plot(x, y)
lines(Monolpoly(x, y, h=0.6, xgrid=gridpts))
##
plot(faithful)
with(faithful, 
lines(Monolpoly(eruptions, waiting, h=0.1, d=1, 
range=c(1.55,5.15))))
# }