Homoscedasticity tests for both low and high-dimensional fixed design   regressions
  This paper is to prove the asymptotic normality of a statistic for detecting the existence of heteroscedasticity for linear regression models without assuming randomness of covariates when the sample size $n$ tends to infinity and the number of covariates $p$ is either fixed or tends to infinity. Moreover our approach indicates that its asymptotic normality holds even without homoscedasticity. 
Zhidong Bai, Guangming Pan, Yanqing Yin
math.ST stat.TH