Variance Estimation for Tree Order Restricted Models
  In this article we discuss estimation of the common variance of several normal populations with tree order restricted means. We discuss the asymptotic properties of the maximum likelihood estimator of the variance as the number of populations tends to infinity. We consider several cases of various orders of the sample sizes and show that the maximum likelihood estimator of the variance may or may not be consistent or be asymptotically normal. 
Antar Bandyopadhyay and Sanjay Chaudhuri
math.ST stat.TH