  We study risk of the minimum norm linear least squares estimator in when the
number of parameters $d$ depends on $n$, and $\frac{d}{n} \rightarrow \infty$.
We assume that data has an underlying low rank structure by restricting
ourselves to spike covariance matrices, where a fixed finite number of
eigenvalues grow with $n$ and are much larger than the rest of the eigenvalues,
which are (asymptotically) in the same order. We show that in this setting risk
of minimum norm least squares estimator vanishes in compare to risk of the null
estimator. We give asymptotic and non asymptotic upper bounds for this risk,
and also leverage the assumption of spike model to give an analysis of the bias
that leads to tighter bounds in compare to previous works.
