On estimation of the noise variance in a high-dimensional signal detection model

When the number of receivers p is large compared to the sample size n, it has been widely observed that standard inference solutions are no longer efficient. In this paper, we address such high-dimensional issues related to the estimation of the noise variance. Several authors have reported that the classical maximum likelihood estimator of the noise variance tends to have a downward bias and this bias is increasingly important when p increases. Using recent results of random matrix theory, we are able to identify the bias. Moreover, a bias-corrected estimator is proposed using this knowledge. The asymptotic normality of the estimator in the high-dimensional context is established.