R code for Tests involving Shape Restrictions

TESTS INVOLVING SHAPE RESTRICTIONS

PART I: Constant vs Monotone Increasing

The model is y_i =f(x_i)+ &epsilon_i, for i=1,...n, where the &epsilon_i are iid mean zero with common variance.

The function f is known to be non-decreasing, interest is in testing H₀: f is constant versus H_a: f is increasing

The traditional test (Robertson, Wright, and Dykstra (1988), chapter 2 or Silvapulle and Sen (2005), chapter 3, does not assume that f is smooth, or even continuous. The code is here:

R code for constant vs increasing regression function

If f can be assumed to be continuous with continuous first derivative, the following test has better power (Meyer (2008)).

R code for constant vs increasing regression function, smoothed alternative

PART II: Linear vs convex regression function

For the unsmoothed alternative, see Meyer (2003)

R code for test of linear vs convex regression function

If f can be assumed to be continuous with continuous first and second derivatives, the following test has better power (Meyer (2008)).

R code for linear vs convex regression function, smoothed alternative

PART III: Monotone vs unconstrained regression function

R code for monotone versus unconstrained, smoothed regression function

meyer@stat.colostate.edu