ABSTRACT
This chapter assumes that the errors are identically distributed. An intermediate level of constraint has g(x) continuous and differentiable, with curves that turn quickly discouraged. One method of fitting under such a constraint is kernel smoothing, and specifically as Nadaraya-Watson smoothing. The documentation for this function indicates that it sometimes fails, and, in fact, dpill failed in this case. This local regression smoother ignored the point with the largest values for each variable, giving the curve a concave rather than convex shape. These data might have been jointly modeled on the square-root scale, to avoid issues relating to the distance of the point with the largest values for each variable from the rest of the data. Many contexts justify a non-decreasing or non-increasing nonparametric relationship between variables. The chpater considers non-decreasing relationships; reversing this constraint is straight-forward. Least squares regression provides parameter estimates minimizing the sum of squares of errors in fitting.
