I have a method which estimates a function with a rate of convergence of n^-(2m/(2m+1)) where n is the number of observations and m is the number of independent variables. However, I would like to estimate this function on the boundary. I would like to make a general assumption about the distribution of data in the space such as uniform, but I do not know the location of the boundary. Do I need to adjust the rate of convergence because I also need to identify the location of the boundary? If so how can I adjust the rate? What is a good textbook to learn the theory behind rate of convergence analysis?