Description Usage Arguments Details Value Author(s) See Also Examples
Compute a univariate concave or convex regression, i.e., for given vectors, x,y,w in R^n, where x has to be strictly sorted (x_1 < x_2 < … < x_n), compute an nvector m minimizing the weighted sum of squares sum(i=1..n; w_i * (y_i  m_i)^2) under the constraints
(m[i]  m[i1])/(x[i]  x[i1]) >= (m[i+1]  m[i])/(x[i+1]  x[i]),
for 1 <= i <= n and
m[0] := m[n+1] := Inf,
for concavity.
For convexity (convex=TRUE
), replace >= by
<= and Inf by +Inf.
1 2 3 4 
x, y 
numeric vectors giving the values of the predictor and
response variable. Alternatively a single “plotting”
structure (twocolumn matrix / yvalues only / list, etc) can be
specified: see 
w 
for 
convex 
logical indicating if convex or concave regression is desired. 
method 
a character string indicating the method used,

tol 
convergence tolerance(s); do not make this too small! 
maxit 
maximal number of (outer and inner) iterations of knot selection. 
adjTol 
(for 
verbose 
logical or integer indicating if (and how much) knot placement and fitting iterations should be “reported”. 
Both algorithms need some numerical tolerances because of rounding
errors in computation of finite difference ratios.
The activeset "Duembgen06_R"
method notably has two different
such tolerances which were both 1e7
= 10^{7} up to March
2016.
The two default tolerances (and the exact convergence checks) may change in the future, possibly to become more adaptive.
an object of class conreg
which is basically a list with components
x 
sorted (and possibly aggregated) abscissa values 
y 
corresponding y values. 
w 
corresponding weights, only for 
yf 
corresponding fitted values. 
convex 
logical indicating if a convex or a concave fit has been computed. 
iKnots 
integer vector giving indices of the knots, i.e. locations where the fitted curve has kinks. Formally, these are exactly those indices where the constraint is fulfilled strictly, i.e., those i where (m[i]  m[i1])/(x[i]  x[i1]) > (m[i+1]  m[i])/(x[i+1]  x[i]). 
call 
the 
iter 
integer (vector of length one or two) with the number of
iterations used (in the outer and inner loop for 
Note that there are several methods defined for conreg
objects,
see predict.conreg
or methods(class = "conreg")
.
Notably print
and plot
; also
predict
, residuals
, fitted
,
knots
.
Also, interpSplineCon()
to construct a more smooth
(cubic) spline, and isIsplineCon()
which checks
if the int is strictly concave or convex the same as the
conreg()
result from which it was constructed.
Lutz Duembgen programmed the original Matlab code in July 2006; Martin Maechler ported it to R, tested, catch infinite loops, added more options, improved tolerance, etc; from April 27, 2007.
isoreg
for isotone (monotone) regression;
CRAN packages ftnonpar, cobs, logcondens.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23  ## Generated data :
N < 100
f < function(X) 4*X*(1  X)
xx < seq(0,1, length=501)# for plotting true f()
set.seed(1)# > conreg does not give convex cubic
x < sort(runif(N))
y < f(x) + 0.2 * rnorm(N)
plot(x,y, cex = 0.6)
lines(xx, f(xx), col = "blue", lty=2)
rc < conreg(x,y)
lines(rc, col = 2, force.iSpl = TRUE)
# 'force.iSpl': force the drawing of the cubic spline through the kinks
title("Concave Regression in R")
y2 < y
## Trivial cases work too:
(r.1 < conreg(1,7))
(r.2 < conreg(1:2,7:6))
(r.3 < conreg(1:3,c(4:5,1)))

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