E[ Y]=0 lim

For M = 2, the best bounds forβ (0.625 β 0.922) were originally established by [1] and later improvedbysomestudies[9]. Infigure (b)thegrid areas indicate the subdomains surrounding the discontinuities, and the light shaded areas denote the neighbouring subdomains around thedarkshaded subdomain. Let Pdiscon bethenumberofthesubdomains lying along the lines, andPtotal be the total number of subdomains. The first experiment: we applied two widely used heteroscedasticity tests, the Park test and the White test to detect the relationships betweenxand = e(the underlying noise, representing the residuals obtained by assumingf() is known). The White test is realized by using polynomials expressedasbelow.