Description Usage Arguments Details Value Author(s) References See Also Examples

A symbolic routine to define that the systematic component *η* is smooth and convex in a predictor in a formula argument to cgam. This is the smooth version.

1 |

`x` |
A numeric predictor which has the same length as the response vector. |

`numknots` |
The number of knots used to constrain |

`knots` |
The knots used to constrain |

`space` |
A character specifying the method to create knots. It will not be used if the user specifies the |

"s.conv" returns the vector "x" and imposes on it five attributes: name, shape, numknots, knots and space.

The name attribute is used in the subroutine plotpersp; the numknots, knots and space attributes are the same as the numknots, knots and space arguments in "s.conv"; the shape attribute is 11("smooth and convex"). According to the value of the vector itself and its shape, numknots, knots and space attributes, the cone edges will be made by C-spline basis functions in Meyer (2008). The cone edges are a set of basis employed in the hinge algorithm.

Note that "s.conv" does not make the corresponding cone edges itself. It sets things up to a subroutine called makedelta in cgam.

See references cited in this section for more details.

The vector x with five attributes, i.e., nm: the name of x; shape: 11 ("smooth and convex"); numknots: the numknots argument in "s.conv"; knots: the knots argument in "s.conv"; space: the space argument in "s.conv".

Mary C. Meyer and Xiyue Liao

Meyer, M. C. (2013b) A simple new algorithm for quadratic programming with applications in statistics. *Communications in Statistics 42(5)*, 1126–1139.

Meyer, M. C. (2008) Inference using shape-restricted regression splines. *Annals of Applied Statistics 2(3)*, 1013–1033.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
# generate y
x <- seq(-1, 2, by = 0.1)
n <- length(x)
y <- x^2 + rnorm(n, .3)
# regress y on x under the shape-restriction: "smooth and convex"
ans <- cgam(y ~ s.conv(x))
knots <- ans$knots[[1]]
# make a plot
plot(x, y)
lines(x, ans$muhat, col = 2)
legend("topleft", bty = "n", "smooth and convex fit", col = 2, lty = 1)
legend(1.6, -1, bty = "o", "knots", pch = "X")
points(knots, 1:length(knots)*0+min(y), pch = "X")
``` |

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