R code for Smoothed Shape-Restricted Regression

# SMOOTHED SHAPE-RESTRICTED LEAST-SQUARES REGRESSION

PART I: monotone regression spline

Given a data vector y in &realn, and a knot specification, minimize ||y &minus &phi||2 for &phi in the set of non-decreasing piece-wise quadratic splines with the specified knots.

The knots themselves may be specified, or a number of (interior) knots specified, which will be placed at equal x quantiles.

The following code has argument y, and returns the least-squares nondecreasing solution.

### R code for monotone spline regression

PART II: convex regression spline

Given a scatterplot of data vector (x,y) where x,y in &realn, minimize ||y &minus &phi||2, for &phi in the set of convex piece-wise cubic splines with the specified knots.

The knots themselves may be specified, or a number of (interior) knots specified, which will be placed at equal x quantiles.

The following code has arguments x and y and returns the solution.

### R code for convex spline regression

PART III: monotone increasing and convex regression spline

Given a scatterplot of data vector (x,y) where x,y in &realn, minimize ||y &minus &phi||2 , for &phi in the set of increasing convex piece-wise cubic splines with the specified knots.

The knots themselves may be specified, or a number of (interior) knots specified, which will be placed at equal x quantiles.

The following code has arguments x and y and returns the solution.

### R code for increasing convex spline regression

PART IV: monotone increasing and concave regression spline

Given a scatterplot of data vector (x,y) where x,y in &realn, minimize ||y &minus &phi||2 , for &phi in the set of increasing concave piece-wise cubic splines with the specified knots.

The knots themselves may be specified, or a number of (interior) knots specified, which will be placed at equal x quantiles.

The following code has arguments x and y and returns the solution.

### R code for increasing concave spline regression

meyer@stat.colostate.edu